How many questions from Kinematics appear in JEE?

Kinematics has appeared in 156 of the last 186 JEE Main and JEE Advanced papers — about 84% of them — contributing 255 questions in total across those papers.

Is Kinematics an important chapter for JEE?

Judged by how often it is actually tested, it appears in roughly 84% of papers. Chapters above about 50% are effectively guaranteed to show up every session, so they repay thorough preparation; lower-frequency chapters are better treated as targeted revision.

Where do these Kinematics questions come from?

Every question is from an official JEE Main or JEE Advanced paper, transcribed from the original paper and tagged to this chapter. Answers follow the official answer key.

Kinematics JEE Previous Year Questions with Answers

Q1·PhysicsMultiple correctJEE Advanced 2026

A particle is thrown with a speed

v

from a point

O

at an angle

\theta

with the horizontal plane such that it passes through the point

P

at a height of 1 m and horizontal distance of 5 m from

O

, as shown in the figure. If acceleration due to gravity is

g

ms

^{-2}

, then the correct statement(s) is/are:

(A)If $\theta = 45^\circ$ , then $v = \frac{5\sqrt{g}}{2}$ ms $^{-1}$ .
(B)If $\theta = 45^\circ$ , the particle reaches its maximum height before it reaches $P$ .
(C)If $\theta = 30^\circ$ , the particle reaches its maximum height after reaching $P$ .
(D)If $\theta = \tan^{-1}\left(\frac{1}{5}\right)$ , then $v = 125\sqrt{g}$ ms $^{-1}$ .

Q2·PhysicsNumericalJEE Main 2026

Two masses of 3.4 kg and 2.5 kg are accelerated from an initial speed of 5 m/s and 12 m/s, respectively. The distances traversed by the masses in the 5

^{\text{th}}

second are 104 m and 129 m, respectively. The ratio of their momenta after 10 s is

\dfrac{x}{8}

. The value of

x

is ________.

Q3·PhysicsSingle correctJEE Main 2026

A gas balloon is going up with a constant velocity of 10 m/s. When this balloon reached a height of 75 m, a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is ________ m. (Take

g = 10

m/s

^2

)

(A)85
(B)150
(C)129
(D)125

Q4·PhysicsSingle correctJEE Main 2026

Two identical bodies, projected with the same speed at two different angles cover the same horizontal range

R

. If the time of flight of these bodies are 5 s and 10 s, respectively, then the value of

R

is ________ m. (Take

g = 10

m/s

^2

)

(A)250
(B)25
(C)500
(D)125

Q5·PhysicsNumericalJEE Main 2026

From 18 m height above the ground a ball is dropped from rest. The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is _____ m. (Take

g = 10

m/s

^{2}

and neglect the air resistance)

Q6·PhysicsSingle correctJEE Main 2026

The velocity (v) versus time (t) plot of a particle is shown in the figure, for a time interval of 40 s. The total distance travelled by the particle and the average velocity during this period are, respectively ________.

(A)25 m and zero
(B)50 m and zero
(C)100 m and zero
(D)100 m and 2.5 m/s

Q7·PhysicsSingle correctJEE Main 2026

Two cars

A

and

B

are moving in the same direction along a straight line with speeds 100 km/h and 80 km/h, respectively such that car

A

is moving ahead of car

B

. A person in car

B

throws a stone with a speed

v

so that it hits the car

A

with a speed of 5 m/s. The value of

v

is ______ km/h.

(A)18
(B)28
(C)38
(D)48

Q8·PhysicsSingle correctJEE Main 2026

If

x

and

y

coordinates of a projectile as a function of time

(t)

are given as

24t

and

43.6t - 4.9t^{2}

, respectively, then the angle (in degrees) made by the projectile with horizontal when

t = 2

s is ______.

(A)60
(B)45
(C)30
(D)75

Q9·PhysicsNumericalJEE Main 2026

A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is 6.4 m. The speed of the bullets from the gun is ______ m/s. (take

g = 10

m/

s^{2}

)

Q10·PhysicsSingle correctJEE Main 2026

Two projectiles are projected with the same initial velocities at the

15^\circ

and

30^\circ

with respect to the horizontal. The ratio of their ranges is

1 : x

. The value of

x

is:

(A) $\sqrt{2}$
(B) $\sqrt{3}$
(C) $2\sqrt{3}$
(D) $\frac{1}{\sqrt{2}}$

Q11·PhysicsSingle correctJEE Main 2026

The velocity of a particle is given as

\vec{v} = -x\hat{i} + 2y\hat{j} - z\hat{k}

m/s. The magnitude of acceleration at point

(1, 2, 4)

is ______ m/s

^{2}

.

(A) $\sqrt{6}$
(B)9
(C) $\sqrt{33}$
(D)0

Q12·PhysicsSingle correctJEE Main 2026

A particle starts moving from time t = 0 and its coordinate is given as

x(t) = 4t^{3} - 3t

. A. The particle returns to its original position (origin) 0.866 units later B. The particle is 1 unit away from origin at its turning point. C. Acceleration of the particle is non-negative. D. The particle is 0.5 units away from origin at its turning point. E. Particle never turns back as acceleration is non-negative. Choose the correct answer from the options given below :

(A)A,C,D only
(B)A,B,C only
(C)C,E only
(D)A,C only

Q13·PhysicsSingle correctJEE Main 2026

Water drops fall from a tap on the floor, 5 m below, at regular intervals of time, the first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from ground, at the instant when the first drop strikes the ground is _______ m. (

g = 10

m/s

^{2}

)

(A)2.5
(B)4.0
(C)4.2
(D)3.8

Q14·PhysicsSingle correctJEE Main 2026

A boy thrown a ball into air at 45° from the horizontal to land it on a roof of a building of height H. If the ball attains maximum height in 2 s and lands on the building in 3 s after launch, then value of H is _________ m.

(g = 10

m/s

^{2})

(A)20
(B)10
(C)25
(D)15

Q15·PhysicsSingle correctJEE Main 2026

The velocity (v) – Distance (x) graph is shown in figure. Which graph represents acceleration (a) versus distance (x) variation of this system?

(A)(1)
(B)(2)
(C)(3)
(D)(4)

Q16·PhysicsSingle correctJEE Main 2026

A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts deaccelerating with 3 m/s

^{2}

. At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is 5 m/s. The initial height of the aeroplane is_____m. (g = 10 m/s

^{2}

)

(A)62.5
(B)92.5
(C)20
(D)82.5

Q17·PhysicsSingle correctJEE Main 2026

An object is projected with kinetic energy K from a point A at an angle 60° with the horizontal. The ratio of the difference in kinetic energies points B and C to that at point A (see figure), in the absence of air friction is :

(A) $1 : 2$
(B) $2 : 3$
(C) $1 : 4$
(D) $3 : 4$

Q18·PhysicsSingle correctJEE Main 2026

A projectile is thrown upward at an angle 60° with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is 45° with the horizontal. The initial speed of the projectile is______m/s.

(A) $40\sqrt{2}$
(B)40
(C) $20\sqrt{3}$
(D) $20\sqrt{2}$

Q19·PhysicsSingle correctJEE Main 2026

A river of width 200 m is flowing from west to east with a speed of 18 km/h. A boat, moving with speed of 36 km/h in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for this journey and also the displacement along the river bank are ______ and ______ respectively.

(A)20 s and 100 m
(B)40 s and 0 m
(C)40 s and 200 m
(D)40 s and 100 m

Q20·PhysicsNumericalJEE Advanced 2025

A projectile of mass 200 g is launched in a viscous medium at an angle 60° with the horizontal, with an initial velocity of 270 m/s. It experiences a viscous drag force

\vec{F} = -c\vec{v}

where the drag coefficient c = 0.1 kg/s and

\vec{v}

is the instantaneous velocity of the projectile. The projectile hits a vertical wall after 2 s . Taking e = 2.7, the horizontal distance of the wall from the point of projection (in m ) is ______

Q21·PhysicsSingle correctJEE Main 2025

Two balls with same mass and initial velocity, are projected at different angles in such a way that maximum height reached by first ball is 8 times higher than that of the second ball.

T_1

and

T_2

are the total flying times of first and second ball, respectively, then the ratio of

T_1

and

T_2

is:

(A) $2\sqrt2:1$
(B) $2:1$
(C) $\sqrt2:1$
(D) $4:1$

Q22·PhysicsSingle correctJEE Main 2025

Two projectiles are fired from ground with same initial speeds from same point at angles

(45^\circ+\alpha)

and

(45^\circ-\alpha)

with horizontal direction. The ratio of their times of flights is

(A)1
(B) $\dfrac{1-\tan\alpha}{1+\tan\alpha}$
(C) $\dfrac{1+\sin2\alpha}{1-\sin2\alpha}$
(D) $\dfrac{1+\tan\alpha}{1-\tan\alpha}$

Q23·PhysicsSingle correctJEE Main 2025

A helicopter flying horizontally with a speed of 360 km/h at an altitude of 2 km, drops an object at an instant. The object hits the ground at a point O, 20 s after it is dropped. Displacement of 'O' from the position of helicopter where the object was released is: (use acceleration due to gravity

g=10

m/s

^2

and neglect air resistance)

(A) $2\sqrt{5}$ km
(B)4 km
(C)7.2 km
(D) $2\sqrt{2}$ km

Q24·PhysicsSingle correctJEE Main 2025

The displacement x versus time t graph is shown below. (A) The average velocity during 0 to 3 s is 10 m/s. (B) The average velocity during 3 to 5 s is 0 m/s. (C) The instantaneous velocity at t = 2 s is 5 m/s. (D) The average velocity during 5 to 7 s and instantaneous velocity at t = 6.5 s are zero. (E) The average velocity from t = 0 to t = 9 s is zero. Choose the correct answer from the options given below:

(A)(A), (D), (E) only
(B)(B), (C), (D) only
(C)(B), (D), (E) only
(D)(B), (C), (E) only

Q25·PhysicsSingle correctJEE Main 2025

If

\vec{L}

and

\vec{P}

represent the angular momentum and linear momentum respectively of a particle of mass

m

having position vector

\vec{r}=a(\hat{i}\cos\omega t+\hat{j}\sin\omega t)

. The direction of force is

(A)Opposite to the direction of $\vec{r}$
(B)Opposite to the direction of $\vec{L}$
(C)Opposite to the direction of $\vec{P}$
(D)Opposite to the direction of $\vec{L}\times\vec{P}$

Q26·PhysicsSingle correctJEE Main 2025

A particle moves along the x-axis and has its displacement

x

varying with time

t

according to the equation

x=c_0(t^2-2)+c(t-2)^2

, where

c_0

and

c

are constants of appropriate dimensions. Then, which of the following statements is correct?

(A)The acceleration of the particle is $2c_0$ .
(B)The acceleration of the particle is $2c$ .
(C)The initial velocity of the particle is $4c$ .
(D)The acceleration of the particle is $2(c+c_0)$ .

Q27·PhysicsSingle correctJEE Main 2025

A particle is projected with velocity

u

so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as

\dfrac{nu^2}{25g}

, where the value of

n

is: (Given '

g

' is the acceleration due to gravity.)

(A)6
(B)18
(C)12
(D)24

Q28·PhysicsSingle correctJEE Main 2025

The angle of projection of a particle is measured from the vertical axis as

\phi

and the maximum height reached by the particle is

h_m

. Here

h_m

as a function of

\phi

can be presented as (choose the correct graph shown in the figure):

(A)(1)
(B)(2)
(C)(3)
(D)(4)

Q29·PhysicsSingle correctJEE Main 2025

Which of the following curves (labelled (A)–(D) in the figure) possibly represent one-dimensional motion of a particle? Choose the correct answer from the options given below:

(A)(A), (B) and (D) only
(B)(A), (B) and (C) only
(C)(A) and (B) only
(D)(A), (C) and (D) only

Q30·PhysicsIntegerJEE Main 2025

A person travelling on a straight line moves with a uniform velocity

v_1

for a distance

x

and with a uniform velocity

v_2

for the next

\dfrac{3}{2}x

distance. The average velocity in this motion is

\dfrac{50}{7}

m/s. If

v_1

is 5 m/s then

v_2=

______ m/s.

Q31·PhysicsSingle correctJEE Main 2025

A sportsman runs around a circular track of radius

r

such that he traverses the path ABAB. The distance travelled and displacement, respectively, are:

(A) $2r,\ 3\pi r$
(B) $3\pi r,\ \pi r$
(C) $\pi r,\ 3r$
(D) $3\pi r,\ 2r$

Q32·PhysicsSingle correctJEE Main 2025

A river is flowing from west to east direction with speed of 9 km h

^{-1}

. If a boat capable of moving at a maximum speed of 27 km h

^{-1}

in still water, crosses the river in half a minute, while moving with maximum speed at an angle of

150^\circ

to direction of river flow, then the width of the river is:

(A)300 m
(B)112.5 m
(C)75 m
(D) $112.5\times\sqrt{3}$ m

Q33·PhysicsIntegerJEE Main 2025

The maximum speed of a boat in still water is 27 km/h. Now this boat is moving downstream in a river flowing at 9 km/h. A man in the boat throws a ball vertically upwards with speed of 10 m/s. Range of the ball as observed by an observer at rest on the river bank, is ______ cm. (Take g = 10 m/s

^2

)

Q34·PhysicsIntegerJEE Main 2025

Two cars P and Q are moving on a road in the same direction. Acceleration of car P increases linearly with time whereas car Q moves with a constant acceleration. Both cars cross each other at time t = 0, for the first time. The maximum possible number of crossing(s) (including the crossing at t = 0) is ______.

Q35·PhysicsSingle correctJEE Main 2025

Two projectiles are fired with same initial speed from same point on ground at angles of

(45^\circ-\alpha)

and

(45^\circ+\alpha)

, respectively, with the horizontal direction. The ratio of their maximum heights attained is:

(A) $\dfrac{1-\tan\alpha}{1+\tan\alpha}$
(B) $\dfrac{1+\sin\alpha}{1-\sin\alpha}$
(C) $\dfrac{1-\sin 2\alpha}{1+\sin 2\alpha}$
(D) $\dfrac{1+\sin 2\alpha}{1-\sin 2\alpha}$

Q36·PhysicsSingle correctJEE Main 2025

The velocity-time graph of an object moving along a straight line is shown in figure. What is the distance covered by the object between t = 0 to t = 4s?

(A)30 m
(B)10 m
(C)13 m
(D)11 m

Q37·PhysicsSingle correctJEE Main 2025

The position vector of a moving body at any instant of time is given as

\vec r=(5t^2\hat i-5t\hat j)

m. The magnitude and direction of velocity at

t=2

s, is,

(A) $5\sqrt{15}$ m/s, making an angle of $\tan^{-1}4$ with $-$ ve Y axis
(B) $5\sqrt{15}$ m/s, making an angle of $\tan^{-1}4$ with $+$ ve X axis
(C) $5\sqrt{17}$ m/s, making an angle of $\tan^{-1}4$ with $-$ ve Y axis
(D) $5\sqrt{17}$ m/s, making an angle of $\tan^{-1}4$ with $+$ ve X axis

Q38·PhysicsSingle correctJEE Main 2025

A ball having kinetic energy KE, is projected at an angle of

60^\circ

from the horizontal. What will be the kinetic energy of ball at the highest point of its flight?

(A) $\dfrac{KE}{8}$
(B) $\dfrac{KE}{4}$
(C) $\dfrac{KE}{16}$
(D) $\dfrac{KE}{2}$

Q39·PhysicsSingle correctJEE Main 2025

The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the first 30.5 second is _______ km.

(A)9
(B)6
(C)3
(D)12

Q40·PhysicsIntegerJEE Main 2025

Two particles are located at equal distance from origin. The position vectors of those are represented by

\vec A=2\hat i+3n\hat j+2\hat k

and

\vec B=2\hat i-2\hat j+4p\hat k

, respectively. If both the vectors are at right angle to each other, the value of

n^{-1}

is _______.

Q41·PhysicsSingle correctJEE Main 2025

A ball of mass 100 g is projected with velocity 20 m/s at

60^\circ

with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is:

(A)20 J
(B)15 J
(C)zero
(D)5 J

Q42·PhysicsIntegerJEE Main 2025

A particle is projected at an angle of 30° from the horizontal at a speed of 60 m/s. The height traversed by the particle in the first second is h₁ and the height traversed in the last second of its upward journey is h₂. The ratio h₁ : h₂ is ______. (take g = 10 m/s²)

Q43·PhysicsNumericalJEE Advanced 2024

A ball is thrown from the location

(x_0, y_0) = (0, 0)

of a horizontal playground with an initial speed

v_0

at an angle

\theta_0

from the +x-direction. The ball is to be hit by a stone, which is thrown at the same time from the location

(x_1, y_1) = (L, 0)

. The stone is thrown at an angle

(180 - \theta_1)

from the +x -direction with a suitable initial speed. For a fixed

v_0

, when

(\theta_0, \theta_1) = (45^0, 45^0)

, the stone hits the ball after time

T_1

, and when

(\theta_0, \theta_1) = (60^0, 30^0)

, it hits the ball after time

T_2

. In such a case,

(T_1/T_2)^2

is ________________

Q44·PhysicsSingle correctJEE Main 2024

A particle moving in a straight line covers half the distance with speed 6 m/s. The other half is covered in two equal time intervals with speeds 9 m/s and 15 m/s respectively. The average speed of the particle during the motion is :

(A)8.8 m/s
(B)10 m/s
(C)9.2 m/s
(D)8 m/s

Q45·PhysicsNumericalJEE Main 2024

If

\vec{a}

and

\vec{b}

makes an angle

\cos^{-1}\left(\frac{5}{9}\right)

with each other, then

|\vec{a}+\vec{b}|=\sqrt{2}\,|\vec{a}-\vec{b}|

for

|\vec{a}|=n\,|\vec{b}|

. The integer value of

n

is ______.

Q46·PhysicsSingle correctJEE Main 2024

Two cars are travelling towards each other at speed of 20 m s

^{-1}

each. When the cars are 300 m apart, both the drivers apply brakes and the cars retard at the rate of 2 m s

^{-2}

. The distance between them when they come to rest is:

(A)200 m
(B)50 m
(C)100 m
(D)25 m

Q47·PhysicsNumericalJEE Main 2024

The resultant of two vectors

\vec{A}

and

\vec{B}

is perpendicular to

\vec{A}

and its magnitude is half of that of

\vec{B}

. The angle between vectors

\vec{A}

and

\vec{B}

is _______ degrees.

Q48·PhysicsSingle correctJEE Main 2024

A particle of mass m moves on a straight line with its velocity increasing with distance according to the equation

v = \alpha\sqrt{x}

, where

\alpha

is a constant. The total work done by all the forces applied on the particle during its displacement from

x = 0

to

x = d

, will be:

(A) $\dfrac{m}{2\alpha^2 d}$
(B) $\dfrac{md}{2\alpha^2}$
(C) $\dfrac{m\alpha^2 d}{2}$
(D) $2m\alpha^2 d$

Q49·PhysicsNumericalJEE Main 2024

A body of mass M thrown horizontally with velocity v from the top of the tower of height H touches the ground at a distance of 100 m from the foot of the tower. A body of mass 2M thrown at a velocity

\dfrac{v}{2}

from the top of the tower of height 4H will touch the ground at a distance of ________ m.

Q50·PhysicsSingle correctJEE Main 2024

The angle of projection for a projectile to have same horizontal range and maximum height is:

(A) $\tan^{-1}(2)$
(B) $\tan^{-1}(4)$
(C) $\tan^{-1}\left(\dfrac{1}{4}\right)$
(D) $\tan^{-1}\left(\dfrac{1}{2}\right)$

Q51·PhysicsSingle correctJEE Main 2024

A clock has

75\,cm

,

60\,cm

long second hand and minute hand respectively. In

30

minutes duration the tip of second hand will travel

x

distance more than the tip of minute hand. The value of

x

in meter is nearly (Take

\pi=3.14

):

(A) $139.4$
(B) $140.5$
(C) $220.0$
(D) $118.9$

Q52·PhysicsNumericalJEE Main 2024

Three vectors

\overrightarrow{OP}

,

\overrightarrow{OQ}

and

\overrightarrow{OR}

each of magnitude

A

are acting as shown in figure. The resultant of the three vectors is

A\sqrt x

. The value of

x

is ___

Q53·PhysicsSingle correctJEE Main 2024

A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in

t_{1}

. If it is projected vertically downwards from the same point with the same speed, it reaches the ground in

t_{2}

. Time required to reach the ground, if it is dropped from the top of the tower, is :

(A) $\sqrt{t_{1}t_{2}}$
(B) $\sqrt{t_{1}-t_{2}}$
(C) $\sqrt{\frac{t_{1}}{t_{2}}}$
(D) $\sqrt{t_{1}+t_{2}}$

Q54·PhysicsNumericalJEE Main 2024

For three vectors

\vec{A}=(-x\hat{i}-6\hat{j}-2\hat{k})

,

\vec{B}=(-\hat{i}+4\hat{j}+3\hat{k})

and

\vec{C}=(-8\hat{i}-\hat{j}+3\hat{k})

, if

\vec{A}\cdot(\vec{B}\times\vec{C})=0

, then the value of

x

is _______.

Q55·PhysicsNumericalJEE Main 2024

A particle moves in a straight line so that its displacement

x

at any time

t

is given by

x^{2}=1+t^{2}

. Its acceleration at any time

t

is

x^{-n}

where

n =

______ .

Q56·PhysicsSingle correctJEE Main 2024

A train starting from rest first accelerates uniformly up to a speed of 80 km/h for time

t

, then it moves with a constant speed for time

3t

. The average speed of the train for this duration of the journey will be (in km/h):

(A) $80$
(B) $70$
(C) $30$
(D) $40$

Q57·PhysicsSingle correctJEE Main 2024

The angle between vector

\vec{Q}

and the resultant of

(2\vec{Q}+2\vec{P})

and

(2\vec{Q}-2\vec{P})

is:

(A) $0^{\circ}$
(B) $\tan^{-1}\left(\dfrac{2\vec{Q}-2\vec{P}}{2\vec{Q}+2\vec{P}}\right)$
(C) $\tan^{-1}\left(\dfrac{P}{Q}\right)$
(D) $\tan^{-1}\left(\dfrac{2Q}{P}\right)$

Q58·PhysicsNumericalJEE Main 2024

A body moves on a frictionless plane starting from rest. If

S_n

is the distance moved between

t = n-1

and

t = n

and

S_{n-1}

is the distance moved between

t = n-2

and

t = n-1

, then the ratio

\dfrac{S_{n-1}}{S_n}

is

\left(1-\dfrac{2}{x}\right)

for

n = 10

. The value of

x

is ___.

Q59·PhysicsSingle correctJEE Main 2024

A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius 9 m and completes 120 revolutions in 3 minutes. The magnitude of the centripetal acceleration of the monkey is (in m/s

^2

):

(A)zero
(B) $16\pi^2$ ms $^{-2}$
(C) $4\pi^2$ ms $^{-2}$
(D) $57600\pi^2$ ms $^{-2}$

Q60·PhysicsNumericalJEE Main 2024

The maximum height reached by a projectile is 64 m. If the initial velocity is halved, the new maximum height of the projectile is __________ m.

Q61·PhysicsNumericalJEE Main 2024

A bus moving along a straight highway with speed of 72 km/h is brought to halt within 4 s after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is ______ m.

Q62·PhysicsSingle correctJEE Main 2024

A cyclist starts from the point P of a circular ground of radius 2 km and travels along its circumference to the point S (shown in the figure). The displacement of a cyclist is

(A)6 km
(B) $\sqrt{8}$ km
(C)4 km
(D)8 km

Q63·PhysicsSingle correctJEE Main 2024

A body travels

102.5\,m

in

n^{th}

second and

115.0\,m

in

(n+2)^{th}

second. The acceleration is:

(A) $9\,m/s^2$
(B) $6.25\,m/s^2$
(C) $12.5\,m/s^2$
(D) $5\,m/s^2$

Q64·PhysicsSingle correctJEE Main 2024

The co-ordinates of a particle moving in x-y plane are given by

x=2+4t

,

y=3t+8t^2

. The motion of the particle is:

(A)non-uniformly accelerated.
(B)uniformly accelerated having motion along a straight line.
(C)uniform motion along a straight line.
(D)uniformly accelerated having motion along a parabolic path.

Q65·PhysicsNumericalJEE Main 2024

A particle is moving in one dimension (along x axis) under the action of a variable force. It's initial position was

16\,m

right of origin. The variation of its position

(x)

with time

(t)

is given as

x=-3t^3+18t^2+16t

, where

x

is in m and

t

is in s. The velocity of the particle when its acceleration becomes zero is ___ m/s.

Q66·PhysicsSingle correctJEE Main 2024

Train A is moving along two parallel rail tracks towards north with speed 72 km/h and train B is moving towards south with speed 108 km/h. Velocity of train B with respect to A and velocity of ground with respect to B are (in ms

^{-1}

):

(A) $-30$ and $50$
(B) $-50$ and $-30$
(C) $-50$ and $30$
(D) $50$ and $-30$

Q67·PhysicsNumericalJEE Main 2024

A particle initially at rest starts moving from reference point

x=0

along x-axis, with velocity

v

that varies as

v=4\sqrt x

m/s. The acceleration of the particle is __________ ms

^{-2}

.

Q68·PhysicsSingle correctJEE Main 2024

A particle moving in a circle of radius

R

with uniform speed takes time

T

to complete one revolution. If this particle is projected with the same velocity at an angle

\theta

to the horizontal, the maximum height attained by it is equal to

4R

. The angle of projection

\theta

is then given by:

(A) $\sin^{-1}\left[\dfrac{2gT^2}{\pi^2 R}\right]^{1/2}$
(B) $\sin^{-1}\left[\dfrac{\pi^2 R}{2gT^2}\right]^{1/2}$
(C) $\cos^{-1}\left[\dfrac{2gT^2}{\pi^2 R}\right]^{1/2}$
(D) $\cos^{-1}\left[\dfrac{\pi R}{2gT^2}\right]^{1/2}$

Q69·PhysicsNumericalJEE Main 2024

A body starts falling freely from height H hits an inclined plane in its path at height h. As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of

\dfrac{H}{h}

for which the body will take the maximum time to reach the ground is ______.

Q70·PhysicsSingle correctJEE Main 2024

If two vectors

\vec{A}

and

\vec{B}

having equal magnitude R are inclined at an angle

\theta

, then

(A) $\left|\vec{A}-\vec{B}\right|=\sqrt{2}\,R\sin\left(\dfrac{\theta}{2}\right)$
(B) $\left|\vec{A}+\vec{B}\right|=2R\sin\left(\dfrac{\theta}{2}\right)$
(C) $\left|\vec{A}+\vec{B}\right|=2R\cos\left(\dfrac{\theta}{2}\right)$
(D) $\left|\vec{A}-\vec{B}\right|=2R\cos\left(\dfrac{\theta}{2}\right)$

Q71·PhysicsSingle correctJEE Main 2024

The relation between time 't' and distance 'x' is

t=\alpha x^2+\beta x

, where

\alpha

and

\beta

are constants. The relation between acceleration (a) and velocity (v) is :

(A) $a=-2\alpha v^3$
(B) $a=-5\alpha v^5$
(C) $a=-3\alpha v^2$
(D) $a=-4\alpha v^4$

Q72·PhysicsNumericalJEE Main 2024

The displacement and the increase in the velocity of a moving particle in the time interval of

t

to

(t+1)\,s

are

125\,m

and

50\,m/s

, respectively. The distance travelled by the particle in

(t+2)^{th}\,s

is ___

m

.

Q73·PhysicsNumericalJEE Main 2024

A vector has magnitude same as that of

\vec{A}=3\hat{i}+4\hat{j}

and is parallel to

\vec{B}=4\hat{i}+3\hat{j}

. The x and y components of this vector in first quadrant are

x

and 3 respectively where

x=

______.

Q74·PhysicsSingle correctJEE Main 2024

A particle is moving in a straight line. The variation of position 'x' as a function of time 't' is given as

x=(t^{3}-6t^{2}+20t+15)

m. The velocity of the body when its acceleration becomes zero is:

(A)4 m/s
(B)8 m/s
(C)10 m/s
(D)6 m/s

Q75·PhysicsSingle correctJEE Main 2024

A body starts moving from rest with constant acceleration covers displacement

S_1

in first

(p-1)

seconds and

S_2

in first

p

seconds. The displacement

S_1+S_2

will be made in time :

(A) $(2p+1)$ s
(B) $\sqrt{2p^2-2p+1}$ s
(C) $(2p-1)$ s
(D) $(2p^2-2p+1)$ s

Q76·PhysicsNumericalJEE Main 2024

A ball rolls off the top of a stairway with horizontal velocity u. The steps are 0.1 m high and 0.1 m wide. The minimum velocity u with which that ball just hits the step 5 of the stairway will be

\sqrt{x}

ms

^{-1}

where

x=

______ [use

g=10

m/s

^2

].

Q77·PhysicsNumericalJEE Main 2024

A body falling under gravity covers two points A and B separated by 80 m in 2 s. The distance of upper point A from the starting point is ________ m. (use

g=10

ms

^{-2}

)

Q78·PhysicsSingle correctJEE Main 2024

Position of an ant (S in metres) moving in Y-Z plane is given by

S=2t^2\hat j+5\hat k

(where

t

is in second). The magnitude and direction of velocity of the ant at

t=1

s will be:

(A)16 m/s in y-direction
(B)4 m/s in x-direction
(C)9 m/s in z-direction
(D)4 m/s in y-direction

Q79·PhysicsNumericalJEE Main 2024

A particle starts from origin at

t=0

with a velocity

5\hat i

m/s and moves in x\textendash y plane under action of a force which produces a constant acceleration of

(3\hat i+2\hat j)

m/s

^2

. If the x-coordinate of the particle at that instant is 84 m, then the speed of the particle at this time is

\sqrt{\alpha}

m/s. The value of

\alpha

is __________.

Q80·PhysicsMultiple correctJEE Advanced 2023

A slide with a frictionless curved surface, which becomes horizontal at its lower end, is fixed on the terrace of a building of height 3 h from the ground, as shown in the figure. A spherical ball of mass m is released on the slide from rest at a height h from the top of the terrace. The ball leaves the slide with a velocity

\vec{u}_0 = u_0\hat{x}

and falls on the ground at a distance d from the building making an angle

\theta

with the horizontal. It bounces off with a velocity

\vec{v}

and reaches a maximum height

h_1

. The acceleration due to gravity is g and the coefficient of restitution of the ground is

1/\sqrt{3}

. Which of the following statement(s) is(are) correct?

(A) $\vec{u}_0 = \sqrt{2gh}\,\hat{x}$
(B) $\vec{v} = \sqrt{2gh}\,(\hat{x} - \hat{z})$
(C) $\theta = 60^0$
(D) $d/h_1 = 2\sqrt{3}$

Q81·PhysicsNumericalJEE Advanced 2023

A person of height 1.6 m is walking away from a lamp post of height 4 m along a straight path on the flat ground. The lamp post and the person are always perpendicular to the ground. If the speed of the person is 60 cm

s^{-1}

, The speed of the tip of the person's shadow on the ground with respect to the person is ________ cm

s^{-1}

Q82·PhysicsSingle correctJEE Main 2023

The position vector of a particle related to time t is given by

\vec{r} = \left(10t\hat{i} + 15t^{2}\hat{j} + 7\hat{k}\right)

m. The direction of net force experienced by the particle is :

(A)Positive y-axis
(B)Positive x-axis
(C)Positive z-axis
(D)In x-y plane

Q83·PhysicsSingle correctJEE Main 2023

The position of a particle related to time is given by

x = (5t^{2} - 4t + 5)

m. The magnitude of velocity of the particle at

t = 2

s will be :

(A)10 ms $^{-1}$
(B)14 ms $^{-1}$
(C)16 ms $^{-1}$
(D)06 ms $^{-1}$

Q84·PhysicsSingle correctJEE Main 2023

A vector in x-y plane makes an angle of

30^\circ

with y-axis. The magnitude of y-component of vector is

2\sqrt{3}

. The magnitude of x-component of the vector will be :

(A) $\frac{1}{\sqrt{3}}$
(B) $6$
(C) $\sqrt{3}$
(D) $2$

Q85·PhysicsSingle correctJEE Main 2023

A passenger sitting in a train A moving at 90 km/h observes another train B moving in the opposite direction for 8 s. If the velocity of the train B is 54 km/h, then length of train B is:

(A)80 m
(B)200 m
(C)120 m
(D)320 m

Q86·PhysicsSingle correctJEE Main 2023

Two trains 'A' and 'B' of length

'l'

and

'4l'

are travelling into a tunnel of length

'L'

in parallel tracks from opposite directions with velocities

108\,km/h

and

72\,km/h

respectively. If train 'A' takes

35\,s

less time than train 'B' to cross the tunnel, then length 'L' of the tunnel is: (Given

L=60\,l

)

(A) $1200\,m$
(B) $2200\,m$
(C) $1800\,m$
(D) $900\,m$

Q87·PhysicsSingle correctJEE Main 2023

The distance travelled by an object in time t is given by

s = (2.5)t^2

. The instantaneous speed of the object at

t = 5

s will be:

(A)12.5 m s $^{-1}$
(B)62.5 m s $^{-1}$
(C)5 m s $^{-1}$
(D)25 m s $^{-1}$

Q88·PhysicsSingle correctJEE Main 2023

A ball is thrown vertically upward with an initial velocity of 150 m/s. The ratio of velocity after 3 s and 5 s is

\dfrac{x+1}{x}

. The value of x is _________. (Take

g=10

m/s

^2

)

(A)6
(B)5
(C)-5
(D)10

Q89·PhysicsSingle correctJEE Main 2023

When the vector

\vec{A}=2\hat{i}+3\hat{j}+2\hat{k}

is subtracted from vector

\vec{B}

, it gives a vector equal to

2\hat{j}

. Then the magnitude of vector

\vec{B}

will be:

(A) $\sqrt{13}$
(B) $3$
(C) $\sqrt{6}$
(D) $\sqrt{5}$

Q90·PhysicsSingle correctJEE Main 2023

From the

v

-

t

graph shown, the ratio of distance to displacement in 25 s of motion

(A) $\dfrac{3}{5}$
(B) $\dfrac{1}{2}$
(C) $\dfrac{5}{3}$
(D) $1$

Q91·PhysicsSingle correctJEE Main 2023

A projectile is projected at

30^\circ

from the horizontal with initial velocity

40

ms

^{-1}

. The velocity of the projectile at

t=2

s from the start will be: (Given

g=10

m/s

^2

)

(A) $20\sqrt{3}$ ms $^{-1}$
(B) $40\sqrt{3}$ ms $^{-1}$
(C) $20$ ms $^{-1}$
(D)Zero

Q92·PhysicsNumericalJEE Main 2023

A projectile fired at

30^{\circ}

to the ground is observed to be at same height at time 3s and 5s after projection, during its flight. The speed of projection of the projectile is ________

\text{ms}^{-1}

(Given

g = 10 \text{ m s}^{-2}

)

Q93·PhysicsSingle correctJEE Main 2023

A person travels

x

distance with velocity

v_1

and then

x

distance with velocity

v_2

in the same direction. If the average velocity of the person is

v

, then the relation between

v

,

v_1

and

v_2

will be:

(A) $v=v_1+v_2$
(B) $v=\tfrac{v_1+v_2}{2}$
(C) $\tfrac{2}{v}=\tfrac{1}{v_1}+\tfrac{1}{v_2}$
(D) $\tfrac{1}{v}=\tfrac{1}{v_1}+\tfrac{1}{v_2}$

Q94·PhysicsSingle correctJEE Main 2023

The range of the projectile projected at an angle of

15°

with horizontal is 50 m. If the projectile is projected with same velocity at an angle of

45°

with horizontal, then the range will be

(A)50 m
(B) $50\sqrt2$ m
(C)100 m
(D) $100\sqrt2$ m

Q95·PhysicsSingle correctJEE Main 2023

The position-time graphs for two students A and B returning from the school to their homes are shown in figure. [Conclusions: (A) A lives closer to the school; (B) B lives closer to the school; (C) A takes lesser time to reach home; (D) A travels faster than B; (E) B travels faster than A.] Choose the correct answer from the options given below:

(A)(A) and (E) only
(B)(B) and (E) only
(C)(A), (C) and (E) only
(D)(A), (D) and (E) only

Q96·PhysicsSingle correctJEE Main 2023

Two projectiles are projected at

30^\circ

and

60^\circ

with the horizontal with the same speed. The ratio of the maximum heights attained by the two projectiles respectively is:

(A) $2:\sqrt{3}$
(B) $\sqrt{3}:1$
(C) $1:3$
(D) $1:\sqrt{3}$

Q97·PhysicsSingle correctJEE Main 2023

The trajectory of a projectile, projected from the ground is given by

y=x-\dfrac{x^{2}}{20}

, where x and y are measured in metre. The maximum height attained by the projectile will be

(A)5 m
(B) $10\sqrt{2}$ m
(C)200 m
(D)10 m

Q98·PhysicsSingle correctJEE Main 2023

Given below are two statements: Statement I: Area under velocity-time graph gives the distance travelled by the body in a given time. Statement II: Area under acceleration-time graph is equal to the change in velocity in the given time. In the light of the given statements, choose the correct answer from the options given below.

(A)Both Statement I and Statement II are true
(B)Statement I is correct but Statement II is false
(C)Statement I is incorrect but Statement II is true
(D)Both Statement I and Statement II are false

Q99·PhysicsSingle correctJEE Main 2023

Two projectiles A and B are thrown with initial velocities of

40

m/s and

60

m/s at angles

30^{\circ}

and

60^{\circ}

with the horizontal respectively. The ratio of their ranges respectively is

(g = 10

m/s

^{2})

(A) $\sqrt{3} : 2$
(B) $2 : \sqrt{3}$
(C) $1 : 1$
(D) $4 : 9$

Q100·PhysicsSingle correctJEE Main 2023

Two forces having magnitude

A

and

\frac{A}{2}

are perpendicular to each other. The magnitude of their resultant is

(A) $\frac{\sqrt{5}A}{4}$
(B) $\frac{5A}{2}$
(C) $\frac{\sqrt{5}A^{2}}{2}$
(D) $\frac{\sqrt{5}A}{2}$

Q101·PhysicsSingle correctJEE Main 2023

As shown in the figure, a particle is moving with constant speed

\pi

m/s. Considering its motion from A to B, the magnitude of the average velocity is:

(A) $\pi$ m/s
(B) $\sqrt{3}$ m/s
(C) $2\sqrt{3}$ m/s
(D) $1.5\sqrt{3}$ m/s

Q102·PhysicsSingle correctJEE Main 2023

A particle starts with an initial velocity of

10.0\,\text{ms}^{-1}

along x-direction and accelerates uniformly at the rate of

2.0\,\text{ms}^{-2}

. The time taken by the particle to reach the velocity of

60.0\,\text{ms}^{-1}

is

(A) $6\,s$
(B) $3\,s$
(C) $30\,s$
(D) $25\,s$

Q103·PhysicsSingle correctJEE Main 2023

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: When a body is projected at an angle

45^\circ

, it's range is maximum. Reason R: For maximum range, the value of

\sin 2\theta

should be equal to one. In the light of the above statements, choose the correct answer from the options given below:

(A)Both A and R are correct but R is NOT the correct explanation of A
(B)Both A and R are correct and R is the correct explanation of A
(C)A is true but R is false
(D)A is false but R is true

Q104·PhysicsSingle correctJEE Main 2023

A particle is moving with constant speed in a circular path. When the particle turns by an angle

90^\circ

, the ratio of instantaneous velocity to its average velocity is

\pi:x\sqrt2

. The value of

x

will be:

(A) $2$
(B) $5$
(C) $1$
(D) $7$

Q105·PhysicsSingle correctJEE Main 2023

A child stands on the edge of the cliff

10

m above the ground and throws a stone horizontally with an initial speed of

5

ms

^{-1}

. Neglecting the air resistance, the speed with which the stone hits the ground will be _______ ms

^{-1}

(given,

g = 10

ms

^{-2}

).

(A) $15$
(B) $20$
(C) $30$
(D) $25$

Q106·PhysicsNumericalJEE Main 2023

For a train engine moving with speed of

20

ms

^{-1}

, the driver must apply brakes at a distance of

500

m before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed

\sqrt{x}

ms

^{-1}

. The value of

x

is _________. (Assuming same retardation is produced by brakes)

Q107·PhysicsSingle correctJEE Main 2023

For a body projected at an angle with the horizontal from the ground, choose the correct statement.

(A)The vertical component of momentum is maximum at the highest point.
(B)The Kinetic Energy (K.E.) is zero at the highest point of projectile motion.
(C)The horizontal component of velocity is zero at the highest point.
(D)Gravitational potential energy is maximum at the highest point.

Q108·PhysicsSingle correctJEE Main 2023

An object moves with speed

v_1

,

v_2

and

v_3

along a line segment

AB

,

BC

and

CD

respectively, where

AB=BC

and

AD=3AB

. Then the average speed of the object will be:

(A) $\tfrac{(v_1+v_2+v_3)}{3v_1v_2v_3}$
(B) $\tfrac{(v_1+v_2+v_3)}{3}$
(C) $\tfrac{3v_1v_2v_3}{(v_1v_2+v_2v_3+v_3v_1)}$
(D) $\tfrac{v_1v_2v_3}{3(v_1v_2+v_2v_3+v_3v_1)}$

Q109·PhysicsSingle correctJEE Main 2023

The initial speed of a projectile fired from ground is

u

. At the highest point during its motion, the speed of projectile is

\frac{\sqrt{3}}{2}u

. The time of flight of the projectile is :

(A) $\frac{2u}{g}$
(B) $\frac{u}{2g}$
(C) $\frac{\sqrt{3}u}{g}$
(D) $\frac{u}{g}$

Q110·PhysicsNumericalJEE Main 2023

The speed of a swimmer is

4\,\text{km h}^{-1}

in still water. If the swimmer makes his strokes normal to the flow of river of width

1

km, he reaches a point

750

m down the stream on the opposite bank. The speed of the river water is __________

\text{kmh}^{-1}

.

Q111·PhysicsSingle correctJEE Main 2023

A body is moving with constant speed, in a circle of radius

10

m. The body completes one revolution in

4

s. At the end of

3^{rd}

second, the displacement of body (in m) from its starting point is:

(A) $15\pi$
(B) $10\sqrt2$
(C) $30$
(D) $5\pi$

Q112·PhysicsNumericalJEE Main 2023

Two bodies are projected from ground with same speeds

40~ms^{-1}

at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of

60°

with horizontal then sum of the maximum heights, attained by the two projectiles, is _________ m. (Given

g=10~ms^{-2}

)

Q113·PhysicsSingle correctJEE Main 2023

A vehicle travels 4 km with a speed of 3 km/h and another 4 km with a speed of 5 km/h, then its average speed is:

(A) $3.50$ km/h
(B) $4.25$ km/h
(C) $4.00$ km/h
(D) $3.75$ km/h

Q114·PhysicsNumericalJEE Main 2023

A horse rider covers half the distance with

5

m/s speed. The remaining part of the distance was travelled with speed

10

m/s for half the time and with speed

15

m/s for other half of the time. The mean speed of the rider averaged over the whole time of motion is

\dfrac{x}{7}

m/s. The value of

x

is

Q115·PhysicsSingle correctJEE Main 2023

Match Column-I (x-t graphs) with Column-II (v-t graphs). Choose the correct answer from the options given below:

Column-I (x-t graphs)	Column-II (v-t graphs)
A.see figure	I.see figure
B.see figure	II.see figure
C.see figure	III.see figure
D.see figure	IV.see figure

(A)A-I, B-II, C-III, D-IV
(B)A-II, B-III, C-IV, D-I
(C)A-I, B-III, C-IV, D-II
(D)A-II, B-IV, C-III, D-I

Q116·PhysicsSingle correctJEE Main 2023

An object moves at a constant speed along a circular path in a horizontal plane with center at the origin. When the object is at

x=+2\,m

, its velocity is

-4\hat j\,m/s

. The object's velocity

(\vec v)

and acceleration

(\vec a_c)

at

x=-2\,m

will be:

(A) $\vec v=-4\hat i\,m/s,\ \vec a=-8\hat j\,m/s^2$
(B) $\vec v=4\hat i\,m/s,\ \vec a=8\hat j\,m/s^2$
(C) $\vec v=4\hat j\,m/s,\ \vec a=8\hat i\,m/s^2$
(D) $\vec v=-4\hat j\,m/s,\ \vec a=8\hat i\,m/s^2$

Q117·PhysicsSingle correctJEE Main 2023

A stone is projected at angle

30^\circ

to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be:

(A)1 : 2
(B)1 : 4
(C)4 : 1
(D)4 : 3

Q118·PhysicsNumericalJEE Main 2023

A tennis ball is dropped on to the floor from a height of 9.8 m. It rebounds to a height 5.0 m. The ball comes in contact with the floor for 0.2 s. The average acceleration during contact is ________ ms

^{-2}

. (Given

g = 10

ms

^{-2}

)

Q119·PhysicsNumericalJEE Main 2023

A car is moving on a circular path of radius

600\,m

such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is moving with an initial speed of

54\,km/hr

is

t\left(1-e^{-\pi/2}\right)s

. The value of

t

is _____.

Q120·PhysicsSingle correctJEE Main 2023

Two objects are projected with same velocity 'u' however at different angles

\alpha

and

\beta

with the horizontal. If

\alpha + \beta = 90^\circ

, the ratio of horizontal range of the first object to the 2nd object will be:

(A) $2:1$
(B) $1:2$
(C) $1:1$
(D) $4:1$

Q121·PhysicsSingle correctJEE Main 2023

A car travels a distance of '

x

' with speed

v_1

and then same distance '

x

' with speed

v_2

in the same direction. The average speed of the car is:

(A) $\dfrac{2v_1 v_2}{v_1+v_2}$
(B) $\dfrac{2x}{v_1+v_2}$
(C) $\dfrac{v_1 v_2}{2(v_1+v_2)}$
(D) $\dfrac{v_1+v_2}{2}$

Q122·PhysicsSingle correctJEE Main 2023

The distance travelled by a particle is related to time t as

x = 4t^2

. The velocity of the particle at

t = 5

s is:

(A) $40$ ms $^{-1}$
(B) $20$ ms $^{-1}$
(C) $8$ ms $^{-1}$
(D) $25$ ms $^{-1}$

Q123·PhysicsNumericalJEE Main 2023

If

\vec{P}=3\hat{i}+\sqrt{3}\hat{j}+2\hat{k}

and

\vec{Q}=4\hat{i}+\sqrt{3}\hat{j}+2.5\hat{k}

, then the unit vector in the direction of

\vec{P}\times\vec{Q}

is

\dfrac{1}{x}(\sqrt{3}\hat{i}+\hat{j}-2\sqrt{3}\hat{k})

. The value of

x

is _______.

Q124·PhysicsSingle correctJEE Main 2023

The velocity time graph of a body moving in a straight line is shown in figure. The ratio of displacement to distance travelled by the body in time

0

to

10

s is:

(A) $1:1$
(B) $1:2$
(C) $1:3$
(D) $1:4$

Q125·PhysicsNumericalJEE Main 2023

Vectors

a\hat{i}+b\hat{j}+\hat{k}

and

2\hat{i}-3\hat{j}+4\hat{k}

are perpendicular to each other when

3a+2b=7

, the ratio of

a

to

b

is

\tfrac{x}{2}

. The value of

x

is _______ .

Q126·PhysicsSingle correctJEE Main 2023

The maximum vertical height to which a man can throw a ball is 136 m. The maximum horizontal distance upto which he can throw the same ball is:

(A)272 m
(B)68 m
(C)192 m
(D)136 m

Q127·PhysicsSingle correctJEE Main 2023

If two vectors

\vec P=\hat i+2m\hat j+m\hat k

and

\vec Q=4\hat i-2\hat j+m\hat k

are perpendicular to each other, then the value of

m

will be:

(A) $-1$
(B) $3$
(C) $2$
(D) $1$

Q128·PhysicsNumericalJEE Advanced 2022

A projectile is fired from horizontal ground with speed v and projection angle

\theta

. When the acceleration due to gravity is g, the range of the projectile is d. If at the highest point in its trajectory, the projectile enters a different region where the effective acceleration due to gravity is

g' = \frac{g}{0.81}

, then the new range is d'=nd. The value of n is __________.

Q129·PhysicsSingle correctJEE Advanced 2022

List I describes four systems, each with two particles A and B in relative motion as shown in figures. List II gives possible magnitudes of their relative velocities (in m s

^{-1}

) at time

t = \frac{\pi}{3}

s. Which one of the following options is correct ?

List-I	List-II
I.A and B are moving on a horizontal circle of radius 1 m with uniform angular speed $\omega = 1$ rad s $^{-1}$ . The initial angular positions of A and B at time t = 0 are $\theta = 0$ and $\theta = \frac{\pi}{2}$ , respectively.	P. $\frac{\sqrt{3}+1}{2}$
II.Projectiles A and B are fired (in the same vertical plane) at t = 0 and t = 0.1 s respectively, with the same speed $v = \frac{5\pi}{\sqrt{2}}$ m s $^{-1}$ and at 45 $^\circ$ from the horizontal plane. The initial separation between A and B is large enough so that they do not collide. (g = 10 m s $^{-2}$ ).	Q. $\frac{\left(\sqrt{3}-1\right)}{\sqrt{2}}$
III.Two harmonic oscillators A and B moving in the x direction according to $x_A = x_0 \sin \frac{t}{t_0}$ and $x_B = x_0 \sin\left(\frac{t}{t_0} + \frac{\pi}{2}\right)$ respectively, starting from t = 0. Take $x_0 = 1$ m, $t_0 = 1$ s.	R. $\sqrt{10}$
IV.Particle A is rotating in a horizontal circular path of radius 1 m on the xy plane, with constant angular speed $\omega = 1$ rad s $^{-1}$ . Particle B is moving up at a constant speed 3 m s $^{-1}$ in the vertical direction as shown in the figure. (Ignore gravity.)	S. $\sqrt{2}$
	T. $\sqrt{25\pi^2+1}$

(A)I $\rightarrow$ R, II $\rightarrow$ T, III $\rightarrow$ P, IV $\rightarrow$ S
(B)I $\rightarrow$ S, II $\rightarrow$ P, III $\rightarrow$ Q, IV $\rightarrow$ R
(C)I $\rightarrow$ S, II $\rightarrow$ T, III $\rightarrow$ P, IV $\rightarrow$ R
(D)I $\rightarrow$ T, II $\rightarrow$ P, III $\rightarrow$ R, IV $\rightarrow$ S

Q130·PhysicsNumericalJEE Main 2022

An object is projected in the air with initial velocity u at an angle

\theta

. The projectile motion is such that the horizontal range R, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be ________degree.

Q131·PhysicsSingle correctJEE Main 2022

A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws n balls per second, the maximum height the balls can reach is

(A)g/2n
(B)g/n
(C)2gn
(D) $g/2n^{2}$

Q132·PhysicsSingle correctJEE Main 2022

If

t = \sqrt{x} + 4

, then

\left(\frac{dx}{dt}\right)_{t=4}

is:

(A)4
(B)Zero
(C)8
(D)16

Q133·PhysicsSingle correctJEE Main 2022

A ball is released from a height h. If

t_1

and

t_2

be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between

t_1

and

t_2

.

(A) $t_1 = \left(\sqrt{2}\right)t_2$
(B) $t_1 = \left(\sqrt{2} - 1\right)t_2$
(C) $t_2 = \left(\sqrt{2} + 1\right)t_1$
(D) $t_2 = \left(\sqrt{2} - 1\right)t_1$

Q134·PhysicsSingle correctJEE Main 2022

A ball is projected with kinetic energy E, at an angle of

60^{0}

to the horizontal. The kinetic energy of this ball at the highest point of its flight will become :

(A)Zero
(B) $\frac{E}{2}$
(C) $\frac{E}{4}$
(D)E

Q135·PhysicsSingle correctJEE Main 2022

A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h. Find the ratio of the times in which it is at height

\frac{h}{3}

while going up and coming down respectively.

(A) $\frac{\sqrt{2}-1}{\sqrt{2}+1}$
(B) $\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$
(C) $\frac{\sqrt{3}-1}{\sqrt{3}+1}$
(D) $\frac{1}{3}$

Q136·PhysicsNumericalJEE Main 2022

A ball is thrown vertically upwards with a velocity of 19.6

\mathrm{ms}^{-1}

from the top of a tower. The ball strikes the ground after 6 s. The height from the ground up to which the ball can rise will be

\left(\dfrac{k}{5}\right)

m. The value of k is ..... (use g = 9.8 m/s

^2

)

Q137·PhysicsSingle correctJEE Main 2022

At time t = 0 a particle starts travelling from a height

7\hat{z}

cm in a plane keeping z coordinate constant. At any instant of time it's position along the x and y directions are defined as 3t and

5t^3

respectively. At t = 1s acceleration of the particle will be

(A) $-30y$
(B) $30y$
(C) $3x + 15y$
(D) $3x + 15y + 7\hat{z}$

Q138·PhysicsSingle correctJEE Main 2022

A NCC parade is going at a uniform speed of 9 km/h under a mango tree on which a monkey is sitting at a height of 19.6 m. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is : (Given g = 9.8 m/s

^{2}

)

(A)5 m
(B)10 m
(C)19.8 m
(D)24.5 m

Q139·PhysicsNumericalJEE Main 2022

If the projection of

2\hat{i}+4\hat{j}-2\hat{k}

on

\hat{i}+2\hat{j}+\alpha\hat{k}

is zero. Then, the value of α will be

Q140·PhysicsSingle correctJEE Main 2022

The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at (4 + x) cm inside the block. The value of x is:

(A)2.0
(B)1.0
(C)0. 5
(D)1.5

Q141·PhysicsSingle correctJEE Main 2022

A body of mass 10 kg is projected at an angle of 45° with the horizontal. The trajectory of the body is observed to pass through a point (20, 10). If T is the time of flight, then its momentum vector, at time

t = \frac{T}{\sqrt{2}}

, is ________ [Take g = 10 m/s

^{2}

]

(A) $100\hat{i} + (100\sqrt{2} - 200)\hat{j}$
(B) $100\sqrt{2}\,\hat{i} + (100 - 200\sqrt{2})\hat{j}$
(C) $100\,\hat{i} + (100 - 200\sqrt{2})\hat{j}$
(D) $100\sqrt{2}\,\hat{i} + (100\sqrt{2} - 200)\hat{j}$

Q142·PhysicsNumericalJEE Main 2022

A ball of mass m is thrown vertically upward. Another ball of mass 2 m is thrown an angle

\theta

with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is

\frac{1}{x}

. The value of x is ______ .

Q143·PhysicsSingle correctJEE Main 2022

A bullet is shot vertically downwards with an initial velocity of 100 m/s from a certain height. Within 10 s, the bullet reaches the ground and instantaneously comes to rest due to the perfectly inelastic collision. The velocity-time curve for total time t = 20 s will be : (Take g = 10 m/s

^{2}

)

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q144·PhysicsNumericalJEE Main 2022

If

\vec{A} = \left(2\hat{i} + 3\hat{j} - \hat{k}\right)

m and

\vec{B} = \left(\hat{i} + 2\hat{j} + 2\hat{k}\right)

m. The magnitude of component of vector

\vec{A}

along vector

\vec{B}

will be________ m.

Q145·PhysicsSingle correctJEE Main 2022

Two projectile thrown at 30

^{0}

and 45

^{0}

with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is

(A)1 : $\sqrt{2}$
(B)2 : 1
(C) $\sqrt{2}$ : 1
(D)1 : 2

Q146·PhysicsSingle correctJEE Main 2022

Two projectiles are thrown with same initial velocity making an angle of

45^\circ

and

30^\circ

with the horizontal respectively. The ratio of their respective ranges will be

(A) $1:\sqrt{2}$
(B) $\sqrt{2}:1$
(C) $2:\sqrt{3}$
(D) $\sqrt{3}:2$

Q147·PhysicsNumericalJEE Main 2022

If the initial velocity in horizontal direction of a projectile is unit vector

\hat{i}

and the equation of trajectory is y = 5x(1 − x). The y component vector of the initial velocity is ______

\hat{j}

(Take g = 10m/s

^{2}

)

Q148·PhysicsSingle correctJEE Main 2022

A person moved from A to B on a circular path as shown in figure. If the distance travelled by him is 60 m, then the magnitude of displacement would be : (Given

\cos 135^\circ = -\,0.7

)

(A)42 m
(B)47 m
(C)19 m
(D)40 m

Q149·PhysicsNumericalJEE Main 2022

A car is moving with speed of 150 km/h and after applying the brake it will move 27 m before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling _______ m distance.

Q150·PhysicsSingle correctJEE Main 2022

Two balls A and B are placed at the top of 180 m tall tower. Ball A is released from the top at t = 0 s. Ball B is thrown vertically down with an initial velocity 'u' at t = 2 s. After a certain time, both balls meet 100 m above the ground. Find the value of 'u' in

ms^{-1}

. [use g = 10

ms^{-2}

] :

(A)10
(B)15
(C)20
(D)30

Q151·PhysicsSingle correctJEE Main 2022

A person can throw a ball upto a maximum range of 100 m. How high above the ground he can throw the same ball?

(A)25 m
(B)50 m
(C)100 m
(D)200 m

Q152·PhysicsSingle correctJEE Main 2022

A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10m in t s,. the distance travelled by the toy in the next t s will be :

(A)10m
(B)20m
(C)30m
(D)40m

Q153·PhysicsSingle correctJEE Main 2022

Two vectors

\vec{A}

and

\vec{B}

have equal magnitudes. If magnitude of

\vec{A}+\vec{B}

is equal to two times the magnitude of

\vec{A}-\vec{B}

, then the angle between

\vec{A}

and

\vec{B}

will be :

(A) $\sin^{-1}\left(\frac{3}{5}\right)$
(B) $\sin^{-1}\left(\frac{1}{3}\right)$
(C) $\cos^{-1}\left(\frac{3}{5}\right)$
(D) $\cos^{-1}\left(\frac{1}{3}\right)$

Q154·PhysicsSingle correctJEE Main 2022

Motion of a particle in x-y plane is described by a set of following equations

x = 4\sin\left(\frac{\pi}{2} - \omega t\right)

m and

y = 4\sin\left(\omega t\right)

m. The path of particle will be –

(A)circular
(B)helical
(C)parabolic
(D)elliptical

Q155·PhysicsNumericalJEE Main 2022

A car covers AB distance with first one–third at velocity v

_1

ms

^{-1}

, second one–third at v

_2

ms

^{-1}

and last one–third at v

_3

ms

^{-1}

. If v

_3

= 3v

_1

, v

_2

= 2v

_1

and v

_1

= 11 ms

^{-1}

then the average velocity of the car is ________ ms

^{-1}

.

Q156·PhysicsSingle correctJEE Main 2022

A projectile is launched at an angle 'α' with the horizontal with a velocity 20 ms

^{-1}

. After 10 s, its inclination with horizontal is 'β'. The value of tanβ will be : (g = 10 ms

^{-2}

)

(A) $\tan\alpha + 5\sec\alpha$
(B) $\tan\alpha - 5\sec\alpha$
(C) $2\tan\alpha - 5\sec\alpha$
(D) $2\tan\alpha + 5\sec\alpha$

Q157·PhysicsSingle correctJEE Main 2022

A girl standing on road holds her umbrella at 45º with the vertical to keep the rain away. If she starts running without umbrella with a speed of

15\sqrt{2}\,kmh^{-1}

, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is :

(A) $30\,kmh^{-1}$
(B) $\frac{25}{\sqrt{2}}kmh^{-1}$
(C) $\frac{30}{\sqrt{2}}kmh^{-1}$
(D) $25\,kmh^{-1}$

Q158·PhysicsSingle correctJEE Main 2022

When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is :

(A)19.6 m
(B)29.4 m
(C)39.2 m
(D)73.5 m

Q159·PhysicsNumericalJEE Main 2022

A ball of mass 0.5 kg is dropped from the height of 10m. The height, at which the magnitude of velocity becomes equal to the magnitude of acceleration due to gravity, is ............... m. (Use g = 10

m/s^{2}

).

Q160·PhysicsNumericalJEE Main 2022

A ball is projected vertically upward with an initial velocity of 50 ms

^{-1}

at t = 0s. At t = 2s. another ball is projected vertically upward with same velocity. At t =________s, second ball will meet the first ball (g =10 ms

^{-2}

).

Q161·PhysicsSingle correctJEE Main 2022

An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero ?

(A)Momentum
(B)Potential energy
(C)Acceleration
(D)Force

Q162·PhysicsNumericalJEE Main 2022

A fighter jet is flying horizontally at a certain altitude with a speed of 200

ms^{-1}

. When it passes directly overhead an anti-aircraft gun, bullet is fired from the gun, at an angle θ with the horizontal, to hit the jet. If the bullet speed is 400 m/s, the value of θ will be ............ °.

Q163·PhysicsSingle correctJEE Main 2022

\vec{A}

is a vector quantity such that

|\vec{A}|

= non-zero constant. Which of the following expressions is true for

\vec{A}

?

(A) $\vec{A}.\vec{A}=0$
(B) $\vec{A}\times\vec{A}<0$
(C) $\vec{A}\times\vec{A}=0$
(D) $\vec{A}\times\vec{A}>0$

Q164·PhysicsSingle correctJEE Main 2022

Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by

X_P(t) = \alpha t + \beta t^2

and

X_Q(t) = ft - t^2

. At what time, both the buses have same velocity ?

(A) $\frac{\alpha - f}{1 + \beta}$
(B) $\frac{\alpha + f}{2(\beta - 1)}$
(C) $\frac{\alpha + f}{2(1 + \beta)}$
(D) $\frac{f - \alpha}{2(1 + \beta)}$

Q165·PhysicsSingle correctJEE Main 2022

For a particle in uniform circular motion, the acceleration

\vec{a}

at any point P(R,θ) on the circular path of radius R is (when θ is measured from the positive x –axis and v is uniform speed) :

(A) $-\frac{v^2}{R}\sin\theta\,\hat{i} + \frac{v^2}{R}\cos\theta\,\hat{j}$
(B) $-\frac{v^2}{R}\cos\theta\,\hat{i} + \frac{v^2}{R}\sin\theta\,\hat{j}$
(C) $-\frac{v^2}{R}\cos\theta\,\hat{i} - \frac{v^2}{R}\sin\theta\,\hat{j}$
(D) $-\frac{v^2}{R}\hat{i} + \frac{v^2}{R}\hat{j}$

Q166·PhysicsSingle correctJEE Main 2022

Which of the following relations is true for two unit vectors

\hat{A}

and

\hat{B}

making an angle θ to each other?

(A) $|\hat{A}+\hat{B}|=|\hat{A}-\hat{B}|\tan\frac{\theta}{2}$
(B) $|\hat{A}-\hat{B}|=|\hat{A}+\hat{B}|\tan\frac{\theta}{2}$
(C) $|\hat{A}+\hat{B}|=|\hat{A}-\hat{B}|\cos\frac{\theta}{2}$
(D) $|\hat{A}-\hat{B}|=|\hat{A}+\hat{B}|\cos\frac{\theta}{2}$

Q167·PhysicsSingle correctJEE Main 2022

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A :Two identical balls A and B thrown with same velocity 'u' at two different angles with horizontal attained the same range R. If A and B reached the maximum height

h_1

and

h_2

respectively, then

R = 4\sqrt{h_1 h_2}

Reason R: Product of said heights.

h_1 h_2 = \left(\frac{u^2 \sin^2 \theta}{2g}\right) \cdot \left(\frac{u^2 \cos^2 \theta}{2g}\right)

Choose the CORRECT answer :

(A)Both A and R are true and R is the correct explanation of A.
(B)Both A and R are true but R is NOT the correct explanation of A.
(C)A is true but R is false
(D)A is false but R is true

Q168·PhysicsNumericalJEE Main 2022

From the top of a tower, a ball is thrown vertically upward which reaches the ground in 6 s. A second ball thrown vertically downward from the same position with the same speed reaches the ground in 1.5 s. A third ball released, from the rest from the same location, will reach the ground in ________ s.

Q169·PhysicsNumericalJEE Main 2022

A body is projected from the ground at an angle of

45^\circ

with the horizontal. Its velocity after 2s is

20

ms

^{-1}

. The maximum height reached by the body during its motion is ________m. (use g

= 10

ms

^{-2}

)

Q170·PhysicsSingle correctJEE Main 2022

A projectile is projected with velocity of 25 m/s at an angle

\theta

with the horizontal. After t seconds its inclination with horizontal becomes zero. If R represents horizontal range of the projectile, the value of

\theta

will be : [use g = 10 m/s

^{2}

]

(A) $\dfrac{1}{2}\sin^{-1}\left(\dfrac{5t^{2}}{4R}\right)$
(B) $\dfrac{1}{2}\sin^{-1}\left(\dfrac{4R}{5t^{2}}\right)$
(C) $\tan^{-1}\left(\dfrac{4t^{2}}{5R}\right)$
(D) $\cot^{-1}\left(\dfrac{R}{20t^{2}}\right)$

Q171·PhysicsNumericalJEE Advanced 2021

A projectile is thrown from a point O on the ground at an angle

45^\circ

from the vertical and with a speed

5\sqrt{2}

m/s. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, 0.5 s after the splitting. The other part, t seconds after the splitting, falls to the ground at a distance x meters from the point O. The acceleration due to gravity

g = 10\,\mathrm{m/s^2}

. The value of t is ______ .

Q172·PhysicsNumericalJEE Advanced 2021

A projectile is thrown from a point O on the ground at an angle

45^\circ

from the vertical and with a speed

5\sqrt{2}

m/s. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, 0.5 s after the splitting. The other part, t seconds after the splitting, falls to the ground at a distance x meters from the point O. The acceleration due to gravity

g = 10\,\mathrm{m/s^2}

. The value of x is ______ .

Q173·PhysicsSingle correctJEE Main 2021

The ranges and heights for two projectiles projected with the same initial velocity at angles 42° and 48° with the horizontal are R

_{1}

, R

_{2}

and H

_{1}

, H

_{2}

respectively. Choose the correct option :

(A)R $_{1}$ > R $_{2}$ and H $_{1}$ = H $_{2}$
(B)R $_{1}$ = R $_{2}$ and H $_{1}$ < H $_{2}$
(C)R $_{1}$ < R $_{2}$ and H $_{1}$ < H $_{2}$
(D)R $_{1}$ = R $_{2}$ and H $_{1}$ = H $_{2}$

Q174·PhysicsNumericalJEE Main 2021

A particle is moving with constant acceleration 'a'. Following graph shows v

^{2}

versus x(displacement) plot. The acceleration of the particle is___m/s

^{2}

.

Q175·PhysicsSingle correctJEE Main 2021

Statement I : Two forces

\left(\vec{P} + \vec{Q}\right)

and

\left(\vec{P} - \vec{Q}\right)

where

\vec{P} \perp \vec{Q}

, when act at an angle

\theta_1

to each other, the magnitude of their resultant is

\sqrt{3(P^2 + Q^2)}

, when they act at an angle

\theta_2

, the magnitude of their resultant becomes

\sqrt{2(P^2 + Q^2)}

. This is possible only when

\theta_1 < \theta_2

. Statement II : In the situation given above.

\theta_1 = 60^\circ

and

\theta_2 = 90^\circ

In the light of the above statements, choose the most appropriate answer from the options given below :-

(A)Statement-I is false but Statement-II is true
(B)Both Statement-I and Statement-II are true
(C)Statement-I is true but Statement-II is false
(D)Both Statement-I and Statement-II are false.

Q176·PhysicsSingle correctJEE Main 2021

A helicopter is flying horizontally with a speed 'v' at an altitude 'h' has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped?

(A) $\sqrt{\frac{2ghv^{2}+1}{h^{2}}}$
(B) $\sqrt{2ghv^{2}+h^{2}}$
(C) $\sqrt{\frac{2v^{2}h}{g}+h^{2}}$
(D) $\sqrt{\frac{2gh}{v^{2}}+h^{2}}$

Q177·PhysicsSingle correctJEE Main 2021

Water drops are falling from a nozzle of a shower onto the floor, from a height of 9.8 m. The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor.

(A)4.18 m
(B)2.94 m
(C)2.45 m
(D)7.35 m

Q178·PhysicsSingle correctJEE Main 2021

A player kicks a football with an initial speed of 25 ms

^{-1}

at an angle of 45° from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? (Take g = 10 ms

^{-2}

)

(A)h $_{max}$ = 10 m, T = 2.5 s
(B)h $_{max}$ = 15.625 m, T = 3.54 s
(C)h $_{max}$ = 15.625 m, T = 1.77 s
(D)h $_{max}$ = 3.54 m, T = 0.125 s

Q179·PhysicsNumericalJEE Main 2021

If the velocity of a body related to displacement x is given by

\upsilon = \sqrt{5000 + 24x}

m/s, then the acceleration of the body is .......

m/s^2

.

Q180·PhysicsNumericalJEE Main 2021

Two spherical balls having equal masses with radius of 5 cm each are thrown upwards along the same vertical direction at an interval of 3s with the same initial velocity of 35 m/s, then these balls collide at a height of .......... m. (Take

g = 10\ \mathrm{m/s^2}

)

Q181·PhysicsSingle correctJEE Main 2021

The angle between vector

\left(\vec{A}\right)

and

\left(\vec{A} - \vec{B}\right)

is :

(A) $\tan^{-1}\left(\frac{-\frac{B}{2}}{A - B\frac{\sqrt{3}}{2}}\right)$
(B) $\tan^{-1}\left(\frac{A}{0.7\,B}\right)$
(C) $\tan^{-1}\left(\frac{\sqrt{3}B}{2A - B}\right)$
(D) $\tan^{-1}\left(\frac{B\cos\theta}{A - B\sin\theta}\right)$

Q182·PhysicsSingle correctJEE Main 2021

A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :

(A)hyperbola
(B)parabola in the direction of motion of plane
(C)straight line vertically down the plane
(D)parabola in a direction opposite to the motion of plane

Q183·PhysicsNumericalJEE Main 2021

A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 30° with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle θ with the line AB should be ________°, so that the swimmer reaches point B.

Q184·PhysicsSingle correctJEE Main 2021

A ball is thrown up with a certain velocity so that it reaches a height 'h'. Find the ratio of the two different times of the ball reaching

\frac{h}{3}

in both the directions.

(A) $\frac{\sqrt{2}-1}{\sqrt{2}+1}$
(B) $\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$
(C) $\frac{\sqrt{3}-1}{\sqrt{3}+1}$
(D) $\frac{1}{3}$

Q185·PhysicsSingle correctJEE Main 2021

Assertion A : If A, B, D are four points on a semi- circular arc with centre at 'O' such that |

\overrightarrow{AB}

| = |

\overrightarrow{BC}

| = |

\overrightarrow{CD}

|, then

\overrightarrow{AB} + \overrightarrow{AC} + \overrightarrow{AD} = 4\overrightarrow{AO} + \overrightarrow{OB} + \overrightarrow{OC}

Reason R : Polygon law of vector addition yields

\overrightarrow{AB} + \overrightarrow{BC} + \overrightarrow{CD} = \overrightarrow{AD} = 2\overrightarrow{AO}

In the light of the above statements, choose the most appropriate answer from the options given below :

(A)A is not correct but R is correct.
(B)A is correct but R is not correct.
(C)Both A and R are correct and R is the correct explanation of A.
(D)Both A and R are correct but R is not the correct explanation of A.

Q186·PhysicsSingle correctJEE Main 2021

Match List I with List II. Choose the correct answer from the options given below :

List-I	List-II
a. $\vec{C}-\vec{A}-\vec{B}=0$	i.(drawn vector diagram — see figure)
b. $\vec{A}-\vec{C}-\vec{B}=0$	ii.(drawn vector diagram — see figure)
c. $\vec{B}-\vec{A}-\vec{C}=0$	iii.(drawn vector diagram — see figure)
d. $\vec{A}+\vec{B}=-\vec{C}$	iv.(drawn vector diagram — see figure)

(A)(a) → (iv), (b) → (i), (c) → (iii), (d) → (ii)
(B)(a) → (iv), (b) → (iii), (c) → (i), (d) → (ii)
(C)(a) → (i), (b) → (iv), (c) → (ii), (d) → (iii)
(D)(a) → (iii), (b) → (ii), (c) → (iv), (d) → (i)

Q187·PhysicsSingle correctJEE Main 2021

The relation between time t and distance x for a moving body is given as

t = mx^2 + nx

, where m and n are constants. The retardation of the motion is : (Where v stands for velocity)

(A) $2n^2v^2$
(B) $2mnv^3$
(C) $2mv^3$
(D) $2nv^3$

Q188·PhysicsSingle correctJEE Main 2021

Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at 4

^{th}

second after its fall to the next droplet is 34.3 m. At what rate the droplets are coming from the tap ? (Take g = 9.8 m/s

^2

)

(A)1 drop / 7 seconds
(B)3 drops / 2 seconds
(C)1 drop / second
(D)2 drops / second

Q189·PhysicsSingle correctJEE Main 2021

A balloon was moving upwards with a uniform velocity of 10 m/s. An object of finite mass is dropped from the balloon when it was at a height of 75 m from the ground level. The height of the balloon from the ground when object strikes the ground was around : (takes the value of g as 10 m /s

^2

)

(A)250 m
(B)300 m
(C)200 m
(D)125 m

Q190·PhysicsSingle correctJEE Main 2021

The instantaneous velocity of a particle moving in a straight line is given as

v = \alpha t + \beta t^2

, where

\alpha

and

\beta

are constants. The distance travelled by the particle between 1s and 2s is :

(A) $\frac{\alpha}{2} + \frac{\beta}{3}$
(B) $\frac{3}{2}\alpha + \frac{7}{3}\beta$
(C) $\frac{3}{2}\alpha + \frac{7}{2}\beta$
(D) $3\alpha + 7\beta$

Q191·PhysicsNumericalJEE Main 2021

Three particles P,Q and R are moving along the vectors

\vec{A} = \hat{i} + \hat{j}

,

\vec{B} = \hat{j} + \hat{k}

and

\vec{C} = -\hat{i} + \hat{j}

respectively. They strike on point and start to move in different directions. Now particle P is moving normal to the plane which contains vector

\vec{A}

and

\vec{B}

. Similarly particle Q is moving normal to the plane which contains vector

\vec{A}

and

\vec{C}

. The angle between the direction of motion of P and Q

\cos^{-1}\left(\frac{1}{\sqrt{x}}\right)

. Then the value of x is ________.

Q192·PhysicsSingle correctJEE Main 2021

What will be the projection of vector

\vec{A}=\hat{i}+\hat{j}+\hat{k}

on vector

\vec{B}=\hat{i}+\hat{j}

?

(A) $2\left(\hat{i}+\hat{j}+\hat{k}\right)$
(B) $\sqrt{2}\left(\hat{i}+\hat{j}\right)$
(C) $\left(\hat{i}+\hat{j}\right)$
(D) $\sqrt{2}\left(\hat{i}+\hat{j}+\hat{k}\right)$

Q193·PhysicsSingle correctJEE Main 2021

If

\vec{A}

and

\vec{B}

are two vectors satisfying the relation

\vec{A}\cdot\vec{B} = \left|\vec{A}\times\vec{B}\right|

. Then the value of

\left|\vec{A}-\vec{B}\right|

will be :

(A) $\sqrt{A^2+B^2-\sqrt{2}AB}$
(B) $\sqrt{A^2+B^2}$
(C) $\sqrt{A^2+B^2+2AB}$
(D) $\sqrt{A^2+B^2+\sqrt{2}AB}$

Q194·PhysicsSingle correctJEE Main 2021

Two vectors

\vec{P}

and

\vec{Q}

have equal magnitudes. If the magnitude of

\vec{P} + \vec{Q}

is n times the magnitude of

\vec{P} - \vec{Q}

, then angle between

\vec{P}

and

\vec{Q}

is :

(A) $\sin^{-1}\left( \dfrac{n^{2}-1}{n^{2}+1} \right)$
(B) $\cos^{-1}\left( \dfrac{n^{2}-1}{n^{2}+1} \right)$
(C) $\sin^{-1}\left( \dfrac{n-1}{n+1} \right)$
(D) $\cos^{-1}\left( \dfrac{n-1}{n+1} \right)$

Q195·PhysicsSingle correctJEE Main 2021

A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time

t_1

. If he remains stationary on a moving escalator then the escalator takes him up in time

t_2

. The time taken by him to walk up on the moving escalator will be :

(A) $\dfrac{t_1 t_2}{t_2 + t_1}$
(B) $t_2 - t_1$
(C) $\dfrac{t_1 + t_2}{2}$
(D) $\dfrac{t_1 t_2}{t_2 - t_1}$

Q196·PhysicsSingle correctJEE Main 2021

A butterfly is flying with a velocity

4\sqrt{2}

m/s in North − East direction. Wind is slowly blowing at 1m/s from North to South. The resultant displacement of the butterfly in 3 seconds is :

(A)15m
(B)20m
(C)3 m
(D) $12\sqrt{2}$ m

Q197·PhysicsSingle correctJEE Main 2021

The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by :

(A)(1)
(B)(2)
(C)(3)
(D)(4)

Q198·PhysicsNumericalJEE Main 2021

The projectile motion of a particle of mass 5 g is shown in the figure. The initial velocity of the particle is

5\sqrt{2}

ms

^{-1}

and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points A and B is x × 10

^{-2}

kgms

^{-1}

. The value of x, to the nearest integer, is _______.

Q199·PhysicsSingle correctJEE Main 2021

The velocity-displacement graph of a particle is shown in the figure. The acceleration-displacement graph of the same particle is represented by :

(A)(1)
(B)(2)
(C)(3)
(D)(4)

Q200·PhysicsNumericalJEE Main 2021

A person is swimming with a speed of 10 m/s at an angle of 120° with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is 'x' m/s. The value of 'x' to the nearest integer is ______.

Q201·PhysicsSingle correctJEE Main 2021

A car accelerates from rest at a constant rate

\alpha

for some time after which it decelerates at a constant rate

\beta

to come to rest. If the total time elapsed is t seconds, the total distance travelled is :

(A) $\frac{4\alpha\beta}{(\alpha+\beta)}t^2$
(B) $\frac{2\alpha\beta}{(\alpha+\beta)}t^2$
(C) $\frac{\alpha\beta}{2(\alpha+\beta)}t^2$
(D) $\frac{\alpha\beta}{4(\alpha+\beta)}t^2$

Q202·PhysicsSingle correctJEE Main 2021

The velocity of a particle is v = v

_{0}

+ gt + Ft

^{2}

. Its position is x = 0 at t = 0 ; then its displacement after time (t = 1) is :

(A)v $_{0}$ + g + F
(B)v $_{0}$ + $\frac{g}{2}$ + $\frac{F}{3}$
(C)v $_{0}$ + $\frac{g}{2}$ + F
(D)v $_{0}$ + 2g + 3F

Q203·PhysicsSingle correctJEE Main 2021

A rubber ball is released from a height of 5 m above the floor. It bounces back repeatedly, always rising to

\frac{81}{100}

of the height through which it falls. Find the average speed of the ball. (Take g = 10 ms

^{-2}

)

(A)3.0 ms $^{-1}$
(B)3.50 ms $^{-1}$
(C)2.0 ms $^{-1}$
(D)2.50 ms $^{-1}$

Q204·PhysicsNumericalJEE Main 2021

A swimmer can swim with velocity of 12 km/h in still water. Water flowing in a river has velocity 6 km/h. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is _________°. (Round off to the Nearest Integer) (find the angle in degree)

Q205·PhysicsSingle correctJEE Main 2021

A scooter accelerates from rest for time t

_{1}

at constant rate a

_{1}

and then retards at constant rate a

_{2}

for time t

_{2}

and comes to rest. The correct value of

\frac{t_{1}}{t_{2}}

will be:

(A) $\frac{a_{1}+a_{2}}{a_{2}}$
(B) $\frac{a_{2}}{a_{1}}$
(C) $\frac{a_{1}+a_{2}}{a_{1}}$
(D) $\frac{a_{1}}{a_{2}}$

Q206·PhysicsSingle correctJEE Main 2021

The trajectory a projectile in a vertical plane is y = αx − βx

^{2}

, where α and β are constants and x & y are respectively the horizontal and vertical distance of the projectile from the point of projection. The angle of projection θ and the maximum height attained H are respectively given by:

(A) $\tan^{-1}\alpha,\ \frac{\alpha^{2}}{4\beta}$
(B) $\tan^{-1}\beta,\ \frac{\alpha^{2}}{2\beta}$
(C) $\tan^{-1}\left(\frac{\beta}{\alpha}\right),\ \frac{\alpha^{2}}{\beta}$
(D) $\tan^{-1}\alpha,\ \frac{4\alpha^{2}}{\beta}$

Q207·PhysicsSingle correctJEE Main 2021

An engine of a train, moving with uniform acceleration, passes the signal post with velocity u and the last compartment with velocity v. The velocity with which middle point of the train passes the signal post is :

(A) $\sqrt{\dfrac{v^2 - u^2}{2}}$
(B) $\dfrac{v - u}{2}$
(C) $\sqrt{\dfrac{v^2 + u^2}{2}}$
(D) $\dfrac{u + v}{2}$

Q208·PhysicsNumericalJEE Main 2021

If P×Q=Q×P, the angle between P and Q is θ(0

^{o}

< θ < 360

^{o}

). The value of 'θ' will be____.

Q209·PhysicsSingle correctJEE Main 2021

In an octagon ABCDEFGH of equal side, what is the sum of

\overrightarrow{AB} + \overrightarrow{AC} + \overrightarrow{AD} + \overrightarrow{AE} + \overrightarrow{AF} + \overrightarrow{AG} + \overrightarrow{AH}

If,

\overrightarrow{AO} = 2\hat{i} + 3\hat{j} - 4\hat{k}

(A) $16\hat{i} + 24\hat{j} - 32\hat{k}$
(B) $-16\hat{i} - 24\hat{j} - 32\hat{k}$
(C) $-16\hat{i} - 24\hat{j} + 32\hat{k}$
(D) $-16\hat{i} + 24\hat{j} + 32\hat{k}$

Q210·PhysicsSingle correctJEE Main 2021

A stone is dropped from the top of a building. When it crosses a point 5m below the top, another stone starts to fall from a point 25m below the top, Both stones reach the bottom of building simultaneously. The height of the building is:

(A)45 m
(B)35 m
(C)25 m
(D)50 m

Q211·PhysicsSingle correctJEE Main 2021

If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph ?

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q212·PhysicsMultiple correctJEE Advanced 2020

Starting at time

t = 0

from the origin with speed

1\ \text{ms}^{-1}

, a particle follows a two-dimensional trajectory in the x-y plane so that its coordinates are related by the equation

y = \frac{x^2}{2}

. The x and y components of its acceleration are denoted by

a_x

and

a_y

, respectively. Then

(A) $a_x = 1\ \text{ms}^{-2}$ implies that when the particle is at the origin, $a_y = 1\ \text{ms}^{-2}$
(B) $a_x = 0$ implies $a_y = 1\ \text{ms}^{-2}$ at all times
(C)at $t = 0$ , the particle's velocity points in the $x$ -direction
(D) $a_x = 0$ implies that at $t = 1$ s, the angle between the particle's velocity and the $x$ axis is $45^\circ$

Q213·PhysicsSingle correctJEE Main 2020

When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed v, he sees that rain drops are coming at an angle 60° from the horizontal. On further increasing the speed of the car to (1 + β)v, this angle changes to 45°. The value of β is close to:

(A)0.50
(B)0.41
(C)0.37
(D)0.73

Q214·PhysicsSingle correctJEE Main 2020

A clock has a continuously moving second's hand of 0.1 m length. The average acceleration of the tip of the hand (in units of

\text{ms}^{-2}

) is of the order of:

(A) $10^{-3}$
(B) $10^{-4}$
(C) $10^{-2}$
(D) $10^{-1}$

Q215·PhysicsSingle correctJEE Main 2020

A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped from the helicopter when it is at a height h. The time taken by the packet to reach the ground is close to [g is the acceleration due to gravity]:

(A) $t = 1.8\sqrt{\dfrac{h}{g}}$
(B) $t = \sqrt{\dfrac{2h}{3g}}$
(C) $t = 3.4\sqrt{\left(\dfrac{h}{g}\right)}$
(D) $t = \dfrac{2}{3}\sqrt{\left(\dfrac{h}{g}\right)}$

Q216·PhysicsSingle correctJEE Main 2020

A balloon is moving up in air vertically above a point A on the ground. When it is at a height

h_1

, a girl standing at a distance d (point B) from A (see figure) sees it at the angle

45^{0}

with respect to the vertical. When the balloon climbs up a future height

h_2

, it is seen at the angle

60^{0}

with respect to the vertical if the girl moves further by a distance 2.464 d (point C). Then the height

h_2

is (given tan

30^{0}

= 0.5774):

(A)0.464 d
(B)0.732 d
(C)1.464 d
(D)d

Q217·PhysicsSingle correctJEE Main 2020

The velocity (v) and time (t) graph of a body in a straight line motion is shown in the figure. The point S is at 4.333 seconds. The total distance covered by the body in 6 s is:

(A)11 m
(B) $\dfrac{37}{3}$ m
(C)12 m
(D) $\dfrac{49}{4}$ m

Q218·PhysicsNumericalJEE Main 2020

The speed verses time graph for a particle is shown in the figure. The distance travelled (in m) by the particle during the time interval t = 0 to t = 5 s will be …..

Q219·PhysicsSingle correctJEE Main 2020

Starting from the origin at time t=0, with initial velocity

5\hat{j}

ms

^{-1}

, a particle moves in the x – y plane with a constant acceleration of

\left(10\hat{i} + 4\hat{j}\right)

ms

^{-2}

. At time t, its coordinates are (20 m,

y_0

m). The values of t and

y_0

are, respectively:

(A)2 s and 24 m
(B)4 s and 52 m
(C)5 s and 25 m
(D)2 s and 18 m

Q220·PhysicsSingle correctJEE Main 2020

A Tennis ball is released from a height h and after freely falling on a wooden floor it rebounds and reaches height

\frac{h}{2}

. The velocity versus height of the ball during its motion may be represented graphically by: (graphs are drawn schematically and on not to scale)

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q221·PhysicsNumericalJEE Main 2020

The distance x covered by a particle in one dimensional motion varies with time t as

x^{2} = at^{2} + bt + c

. If the acceleration of the particle depends on x as

x^{-n}

, where n is an integer, the value of n is ____.

Q222·PhysicsSingle correctJEE Main 2020

A particle starts from the origin at t = 0 with an initial velocity of 3.0

\hat{i}

m/s and moves in the x-y plane with a constant acceleration

(6.0\hat{i}+4.0\hat{j})

m/s

^{2}

. The x-coordinate of the particle at the instant when its y-coordinate is 32 m is D meters. The value of D is

(A)40
(B)60
(C)32
(D)50

Q223·PhysicsNumericalJEE Main 2020

A particle is moving along the x-axis with its coordinate with time 't' given by

x(t) = 10 + 8t - 3t^{2}

. Another particle is moving along the y-axis with its coordinate a function of time given by

y(t) = 5 - 8t^{3}

. At t = 1 s, the speed of the second particle as measured in the frame of the first particle is given as

\sqrt{v}

. Then v (in m/s) is ___________.

Q224·PhysicsSingle correctJEE Main 2020

A particle moves such that its position vector

\vec{r}(t)=\cos\omega \hat{i}+\sin\omega t\hat{j}

where

\omega

is a constant and t is time. Then which of the following statements is true for the velocity

\vec{v}(t)

and acceleration

\vec{a}(t)

of the particle:

(A) $\vec{v}$ is perpendicular to $\vec{r}$ and $\vec{a}$ is directed towards the origin.
(B) $\vec{v}$ and $\vec{a}$ both are parallel to $\vec{r}$
(C) $\vec{v}$ is perpendicular to $\vec{r}$ and $\vec{a}$ is directed away from the origin.
(D) $\vec{v}$ and $\vec{a}$ both are perpendicular to $\vec{r}$

Q225·PhysicsNumericalJEE Main 2020

The sum of two forces

\vec{P}

and

\vec{Q}

is

\vec{R}

such that

|\vec{R}| = |\vec{P}|

. The angle

\theta

(in degrees) that the resultant of

2\vec{P}

and

\vec{Q}

will make with

\vec{Q}

is, __________.

Q226·PhysicsNumericalJEE Advanced 2019

A ball is thrown from ground at an angle

\theta

with horizontal and with an initial speed

u_0

. For the resulting projectile motion, the magnitude of average velocity of the ball up to the point when it hits the ground for the first time is

V_1

. After hitting the ground, the ball rebounds at the same angle

\theta

but with a reduced speed of

u_0/\alpha

. Its motion continues for a long time as shown in figure. If the magnitude of average velocity of the ball for entire duration of motion is

0.8 V_1

, the value of

\alpha

is_________.

Q227·PhysicsSingle correctJEE Main 2019

The trajectory of a projectile near the surface of the earth is given as y = 2x

-

9x

^{2}

. If it were launched at an angle

\theta_0

with speed v

_0

then (g = 10 ms

^{-2}

) :

(A) $\theta_0 = \cos^{-1}\left(\dfrac{1}{\sqrt{5}}\right)$ and v $_0$ = $\dfrac{5}{3}$ ms $^{-1}$
(B) $\theta_0 = \cos^{-1}\left(\dfrac{2}{\sqrt{5}}\right)$ and v $_0$ = $\dfrac{3}{5}$ ms $^{-1}$
(C) $\theta_0 = \sin^{-1}\left(\dfrac{2}{\sqrt{5}}\right)$ and v $_0$ = $\dfrac{3}{5}$ ms $^{-1}$
(D) $\theta_0 = \sin^{-1}\left(\dfrac{1}{\sqrt{5}}\right)$ and v $_0$ = $\dfrac{5}{3}$ ms $^{-1}$

Q228·PhysicsSingle correctJEE Main 2019

A particle is moving with speed v = v

\sqrt{x}

along positive x-axis. Calculate the speed of the particle at time t = t (assume that the particle is at origin at t = 0).

(A)b $^{2}$ τ
(B) $\dfrac{b^{2}\tau}{2}$
(C) $\dfrac{b^{2}\tau}{\sqrt{2}}$
(D) $\dfrac{b^{2}\tau}{4}$

Q229·PhysicsSingle correctJEE Main 2019

A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If

t_1

and

t_2

are the values of the time taken by it to hit the target in two possible ways, the product

t_1t_2

is:

(A)2R / g
(B)R / 4g
(C)R / g
(D)R/2g

Q230·PhysicsSingle correctJEE Main 2019

Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights, h

_{1}

and h

_{2}

. Which of the following is correct?

(A)R $^{2}$ = 4 h $_{1}$ h $_{2}$
(B)R $^{2}$ = 2 h $_{1}$ h $_{2}$
(C)R $^{2}$ = 16 h $_{1}$ h $_{2}$
(D)R $^{2}$ = h $_{1}$ h $_{2}$

Q231·PhysicsSingle correctJEE Main 2019

A plane is inclined at an angle α = 30° with respect to the horizontal. A particle is projected with a speed u = 2 ms

^{-1}

, from the base of the plant, making an angle θ = 15° with respect to the plane as shown in the figure. The distance from the base at which the particle hits the plane is close to (Take g = 10 ms

^{2}

)

(A)18 cm
(B)14 cm
(C)26 cm
(D)20 cm

Q232·PhysicsSingle correctJEE Main 2019

The position of a particle as a function of time t, is given by

x(t) = at + bt^{2} - ct^{3}

where a, b and c are constants. When the particle attains zero acceleration, then its velocity will be:

(A) $a + \dfrac{b^{2}}{4c}$
(B) $a + \dfrac{b^{2}}{c}$
(C) $a + \dfrac{b^{2}}{2c}$
(D) $a + \dfrac{b^{2}}{3c}$

Q233·PhysicsSingle correctJEE Main 2019

The position vector of a particle changes with time according to the relation

\vec{r}(t) = 15t^{2}\hat{i} + (4 - 20t^{2})\hat{j}

. What is the magnitude of the acceleration at t = 1?

(A)40
(B)100
(C)25
(D)50

Q234·PhysicsSingle correctJEE Main 2019

The stream of a river is flowing with a speed of 2 km/h. A swimmer can swim at a speed of 4 km/h. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight?

(A)60°
(B)90°
(C)120°
(D)150°

Q235·PhysicsSingle correctJEE Main 2019

A ball is thrown vertically up (taken as +z-axis) from the ground. The correct momentum-height (p-h) diagram is:

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q236·PhysicsSingle correctJEE Main 2019

Ship A is sailing towards north-east with velocity

\vec{v}=30\hat{i}+50\hat{j}

km/hr where

\hat{i}

points east and

\hat{j}

, north. Ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing towards west at 10 km/hr. A will be at minimum distance from B ins:

(A)2.2 hrs.
(B)4.2 hrs.
(C)2.6 hrs.
(D)3.2 hrs.

Q237·PhysicsSingle correctJEE Main 2019

Let

|\vec{A}_1| = 3, |\vec{A}_2| = 5

, and

|\vec{A}_1 + \vec{A}_2| = 5

. The value of

(2\vec{A}_1 + 3\vec{A}_2)\cdot(3\vec{A}_1 - 2\vec{A}_2)

is:

(A) $-106.5$
(B) $-112.5$
(C) $-118.5$
(D) $-99.5$

Q238·PhysicsSingle correctJEE Main 2019

A particle starts from origin O from rest and moves with a uniform acceleration along the positive x

-

axis. Identify all figures that correctly represent the motion qualitatively. (a = acceleration, v = velocity, x = displacement, t = time)

(A)a, b, c
(B)a
(C)b, c
(D)a, b, d

Q239·PhysicsSingle correctJEE Main 2019

A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr. The ratio of times taken by the passenger train to completely cross the freight train when: (i) they are moving in the same direction, and (ii) in the opposite directions is:

(A) $\frac{11}{5}$
(B) $\frac{5}{2}$
(C) $\frac{3}{2}$
(D) $\frac{25}{11}$

Q240·PhysicsSingle correctJEE Main 2019

Two particles A, B are moving on two concentric circles of radii R

_{1}

and R

_{2}

with equal angular speed ω. At t = 0, their positions and direction of motion are shown in the figure : The relative velocity

\vec{v}_{A} - \vec{v}_{B}

at

t = \frac{\pi}{2\omega}

is given by :

(A) $\omega(R_{1} + R_{2})\hat{i}$
(B) $-\omega(R_{1} + R_{2})\hat{i}$
(C) $\omega(R_{2} - R_{1})\hat{i}$
(D) $\omega(R_{1} - R_{2})\hat{i}$

Q241·PhysicsSingle correctJEE Main 2019

A body is projected at t = 0 with a velocity 10 ms

^{-1}

at an angle of 60

^{0}

with the horizontal. The radius of curvature of its trajectory at t = 1s is R. Neglecting air resistance and taking acceleration due to gravity g = 10 ms

^{-2}

, the radius of R is:

(A)10.3 m
(B)2.8 m
(C)2.5 m
(D)5.1 m

Q242·PhysicsSingle correctJEE Main 2019

A particle is moving along a circular path with a constant speed of 10 ms

^{-1}

. What is the magnitude of the change in velocity of the particle, when it moves through an angle of 60

^{0}

around the centre of the circle?

(A) $10\sqrt{3}$ m/s
(B)0
(C) $10\sqrt{2}$ m/s
(D)10 m/s

Q243·PhysicsSingle correctJEE Main 2019

A particle moves from the point

(2.0\hat{i}+4.0\hat{j})

m, at t = 0 with an initial velocity

(5.0\hat{i}+4.0\hat{j})

ms

^{-1}

. It is acted upon by a constant force which produces a constant acceleration

(4.0\hat{i}+4.0\hat{j})

ms

^{-2}

. What is the distance of the particle from the origin at time 2s?

(A)15m
(B) $20\sqrt{2}$ m
(C)5m
(D) $10\sqrt{2}$ m

Q244·PhysicsSingle correctJEE Main 2019

In the cube of side 'a' shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be:

(A) $\dfrac{1}{2}$ a $\left(\hat{k}-\hat{i}\right)$
(B) $\dfrac{1}{2}$ a $\left(\hat{i}-\hat{k}\right)$
(C) $\dfrac{1}{2}$ a $\left(\hat{j}-\hat{i}\right)$
(D) $\dfrac{1}{2}$ a $\left(\hat{j}-\hat{k}\right)$

Q245·PhysicsSingle correctJEE Main 2019

Two guns A and B can fire bullets at speed 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is:

(A)1 : 16
(B)1 : 2
(C)1 : 4
(D)1 : 8

Q246·PhysicsSingle correctJEE Main 2019

A particle is moving with a velocity

\vec{v} = K(y\hat{i} + x\hat{j})

, where K is a constant. The general equation for its path is:

(A) $y = x^{2}$ + constant
(B) $y^{2} = x$ + constant
(C) $y^{2} = x^{2}$ + constant
(D)xy = constant

Q247·PhysicsSingle correctJEE Main 2019

In a car race on straight road, car A takes a time ‘t’ less than car B at the finish and passes finishing point with a speed ‘v’ more than that of car B. Both the cars start from rest and travel with constant acceleration a

_1

and a

_2

respectively. Then ‘v’ is equal to

(A) $\dfrac{2a_1a_1}{a_1+a_2}\,t$
(B) $\sqrt{2a_1a_2}\,t$
(C) $\sqrt{a_1a_2}\,t$
(D) $\dfrac{a_1+a_2}{2}\,t$

Q248·PhysicsSingle correctJEE Main 2019

The position co-ordinates of a particle moving in a 3-D coordinates system is given by

x = a\cos\omega t

y = a\sin\omega t

and

z = a\omega t

The speed of the particle is:

(A) $\sqrt{2}\,a\omega$
(B) $a\omega$
(C) $\sqrt{3}\,a\omega$
(D) $2a\omega$

Q249·PhysicsNumericalJEE Advanced 2018

A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass

m = 0.4

kg is at rest on this surface. An impulse of 1.0 Ns is applied to the block at time t = 0 so that it starts moving along the x-axis with a velocity

v(t) = v_{0}e^{-t/\tau}

, where

v_{0}

is a constant and

\tau

= 4 s. The displacement of the block, in meters, at t =

\tau

is __________. Take

e^{-1}

= 0.37.

Q250·PhysicsNumericalJEE Advanced 2018

A ball is projected from the ground at an angle of

45^{\circ}

with the horizontal surface. It reaches a maximum height of 120

m

and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of the ball makes an angle of

30^{\circ}

with the horizontal surface. The maximum height it reaches after the bounce, in metres, is ____________.

Q251·PhysicsNumericalJEE Advanced 2018

Two vectors

\vec{A}

and

\vec{B}

are defined as

\vec{A} = a\hat{i}

and

\vec{B} = a\left(\cos\omega t\,\hat{i} + \sin\omega t\,\hat{j}\right)

, where

a

is a constant and

\omega = \pi/6\ rad\ s^{-1}

. If

\left|\vec{A} + \vec{B}\right| = \sqrt{3}\left|\vec{A} - \vec{B}\right|

at time

t = \tau

for the first time, the value of

\tau

, in seconds, is ______.

Q252·PhysicsSingle correctJEE Advanced 2017

Three vectors

\vec{P}

,

\vec{Q}

and

\vec{R}

are shown in the figure. Let

S

be any point on the vector

\vec{R}

. The distance between the point

P

ad

S

is

b|\vec{R}|

. The general relation among vectors

\vec{P}

,

\vec{Q}

and

\vec{S}

is

(A) $\vec{S} = (1-b)\vec{P} + b\vec{Q}$
(B) $\vec{S} = (b-1)\vec{P} + b\vec{Q}$
(C) $\vec{S} = (1-b^{2})\vec{P} + b\vec{Q}$
(D) $\vec{S} = (1-b)\vec{P} + b^{2}\vec{Q}$

Q253·PhysicsSingle correctJEE Advanced 2017

Consider an expanding sphere of instantaneous radius

R

whose total mass remains constant. The expansion is such that the instantaneous density

\rho

remains uniform throughout the volume. The rate of fractional change in density

\left(\dfrac{1}{\rho}\dfrac{d\rho}{dt}\right)

is constant. The velocity

v

of any point on the surface of the expanding sphere is proportional to

(A) $R$
(B) $R^{3}$
(C) $\dfrac{1}{R}$
(D) $R^{2/3}$

Q254·PhysicsIntegerJEE Advanced 2014

A rocket is moving in a gravity free space with a constant acceleration of

2 \text{ ms}^{-2}

along

+ x

direction (see figure). The length of a chamber inside the rocket is

4 \text{ m}

. A ball is thrown from the left end of the chamber in

+ x

direction with a speed of

0.3 \text{ ms}^{-1}

relative to the rocket. At the same time, another ball is thrown in

-x

direction with a speed of

0.2 \text{ ms}^{-1}

from its right end relative to the rocket. The time in seconds when the two balls hit each other is

Q255·PhysicsIntegerJEE Advanced 2014

Airplanes

A

and

B

are flying with constant velocity in the same vertical plane at angles

30^{\circ}

and

60^{\circ}

with respect to the horizontal respectively as shown in the figure. The speed of

A

is

100\sqrt{3} \text{ ms}^{-1}

. At time

t = 0 \text{ s}

, an observer in

A

finds

B

at a distance of

500 \text{ m}

. This observer sees

B

moving with a constant velocity perpendicular to the line of motion of

A

. If at

t = t_0

,

A

just escapes being hit by

B

,

t_0

in seconds is

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