JEE Main Previous Year Questions (2021-22): Momentum & Impulse | 35 Years Chapter wise Previous Year Solved Papers for JEE PDF Download

Q.1. If momentum of a body is increased by 20%, then its kinetic energy increases by     (JEE Main 2022)
(a) 36%
(b) 40%
(c) 44%
(d) 48%

Ans. c
Let, initial momentum of body (p_i) = p
∴ Final momentum (p_f) = p_i + 20% of p_i
= p + 0.2 p
= 1.2 p
We know,
Kinetic energy (E) = p²/2m
∴ E_i = p²/2m

∴ % Change in kinetic energy

Q.2. Two bodies of mass 1 kg and 3 kg have position vectors  and  respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector :      (JEE Main 2022)
(a)
(b)
(c)
(d)

Ans. a

Q.3. In two different experiments, an object of mass 5 kg moving with a speed of 25 ms⁻¹ hits two different walls and comes to rest within (i) 3 second, (ii) 5 seconds, respectively. Choose the correct option out of the following :      (JEE Main 2022)
(a) Impulse and average force acting on the object will be same for both the cases.
(b) Impulse will be same for both the cases but the average force will be different.
(c) Average force will be same for both the cases but the impulse will be different.
(d) Average force and impulse will be different for both the cases.

Ans. b
ΔP = impulse = same since acceleration is different force acting will be different.

Q.4. 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 = T/√2, is _____________.    
[Take g = 10 m/s²]            (JEE Main 2022)
(a)
(b)
(c)
(d)

Ans. d
m = 10 kg
θ = 45^∘


⇒ R = 40
40 = u²/10 ⇒ u = 20

Q.5. A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momentum will be :      (JEE Main 2022)
(a) 1 : 1
(b) 2 : 1
(c) 1 : 4
(d) 4 : 1

Ans. b

Q.6. A ball of mass 0.15 kg hits the wall with its initial speed of 12 ms⁻¹ and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is 100 N, calculate the time duration of the contact of ball with the wall.      (JEE Main 2022)
(a) 0.018 s
(b) 0.036 s
(c) 0.009 s
(d) 0.072 s

Ans. b
F = 100 N
ΔP = 2 × 0.15 × 12
= 3.6
⇒ t = 3.6/100 = 0.036 s

Q.7. Two billiard balls of mass 0.05 kg each moving in opposite directions with 10 ms⁻¹ collide and rebound with the same speed. If the time duration of contact is t = 0.005 s, then what is the force exerted on the ball due to each other?      (JEE Main 2022)
(a) 100 N
(b) 200 N
(c) 300 N
(d) 400 N

Ans. b
Change in momentum of one ball
= 2 × (0.05)(10) kg m/s
= 1 kg m/s

= 200 N

Q.8. Two bodies A and B of masses 5 kg and 8 kg are moving such that the momentum of body B is twice that of the body A. The ratio of their kinetic energies will be :      (JEE Main 2022)
(a) 4 : 5
(b) 2 : 5
(c) 5 : 4
(d) 5 : 2

Ans. b
Given,
Mass of body A = 5 kg
Mass of body B = 8 kg
Momentum of body B is twice that of body A,
∴ P_B = 2P_A
We know,
Kinetic Energy (K) = P²/2m



= 2/5

Q.9. If force   acts on a particle position vector  then, the torque about the origin will be :      (JEE Main 2022)
(a)
(b)
(c)
(d)

Ans. b

Q.10. An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero?      (JEE Main 2022)
(a) Momentum
(b) Potential Energy
(c) Acceleration
(d) Force

Ans. a
At maximum height it's velocity is zero. So momentum (mv) will be zero.

Q.11. Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates (0, 0) cm and (x, 0) cm respectively. The block of 10 kg is moved on the same line through a distance of 6 cm towards the other block. The distance through which the block of 30 kg must be moved to keep the position of centre of mass of the system unchanged is :      (JEE Main 2022)
(a) 4 cm towards the 10 kg block
(b) 2 cm away from the 10 kg block
(c) 2 cm towards the 10 kg block
(d) 4 cm away from the 10 kg block

Ans. c
For COM to remain unchanged,
m₁x₁ = m₂x₂
⇒ 10 × 6 = 30 × x2
⇒ x₂ = 2 cm towards 10 kg block.

Q.12. A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of 1 kgs⁻¹ and at a speed of 10 ms⁻¹. Then, the initial acceleration of the block, in ms⁻², will be :             (JEE Main 2022)
(a) 3
(b) 6
(c) 5
(d) 4

Ans. c
F = ρ v²a
⇒ 10 × 1 = 2 × acceleration
⇒ Acc. = 5 m/s²   

Q.13. The distance of centre of mass from end A of a one dimensional rod (AB) having mass density  and length L (in meter) is The value of α is ___________. (where x is the distance from end A)              (JEE Main 2022)

Ans. 8


⇒ α = 8

Q.14. A batsman hits back a ball of mass 0.4 kg straight in the direction of the bowler without changing its initial speed of 15 ms−1. The impulse imparted to the ball is ___________ Ns.             (JEE Main 2022)

Ans. 12
l = mΔv
= 0.4 × 2 × 15 = 12 Ns

Q.15. A rolling wheel of 12 kg is on an inclined plane at position P and connected to a mass of 3 kg through a string of fixed length and pulley as shown in figure. Consider PR as friction free surface. The velocity of centre of mass of the wheel when it reaches at the bottom Q of the inclined plane PQ will be 12xgh m/s. The value of x is ___________.             (JEE Main 2022)

Ans. 3
For rolling wheel

Q.16. A pendulum consists of a bob of mass m = 0.1 kg and a massless inextensible string of length L = 1.0 m. It is suspended from a fixed point at height H = 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse P = 0.2 kg-m/s is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is J kg-m²/s. The kinetic energy of the pendulum just after the lift-off is K Joules.
The value of J is ___________.       (JEE Advanced 2021)

Ans. 0.18
Angular momentum, L = P × 0.9 = 0.18 kgm²/s

Q.17. A pendulum consists of a bob of mass m = 0.1 kg and a massless inextensible string of length L = 1.0 m. It is suspended from a fixed point at height H = 0.9 m above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse P = 0.2 kg-m/s is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is J kg-m²/s. The kinetic energy of the pendulum just after the lift-off is K Joules.
The value of K is ___________.       (JEE Advanced 2021)

Ans. 0.16
Angular momentum, L = P × 0.9 = 0.18 kgm²/s
Just after string becomes taut; there will be no velocity along the string.

Q.18. One end of a horizontal uniform beam of weight W and length L is hinged on a vertical wall at point O and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point Q, at a height L above the hinge at point O. A block of weight αW is attached at the point P of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of (2√2)W. Which of the following statement(s) is(are) correct?       (JEE Advanced 2021)
(a) The vertical component of reaction force at O does not depend on α
(b) The horizontal component of reaction force at O is equal to W for α = 0.5
(c) The tension in the rope is 2W for α = 0.5
(d) The rope breaks if α > 1.5

Ans. (a, b, d)
Free body diagram of rod
∑F_x = 0
R₁ = T cos ⁡45^∘
R₁ =T/√2 ..... (i)
∑F_y = 0
R₂ + T sin ⁡45^∘ = W + αW

∑τ₀ = 0


From Eqs. (ii) and (iii), we get

R₂ = W₂
Hence, option (a) is correct.
From Eqs. (i) and (iii), we get

α = 0.5, R₁ = W
Hence, option (b) is correct.
From Eq. (iii), if α = 0.5


For rope to break,


Hence, option (d) is correct.

Q.19.  A particle of mass M = 0.2 kg is initially at rest in the xy-plane at a point (x = −l, y = −h), where l = 10 m and h = 1 m. The particle is accelerated at time t = 0 with a constant acceleration a = 10 m/s² along the positive x-direction. Its angular momentum and torque with respect to the origin, in SI units, are represented by  respectively.  are unit vectors along the positive x, y and z-directions, respectively. If  then which of the following statement(s) is(are) correct?       (JEE Advanced 2021)
(a) The particle arrives at the point (x = l, y = −h) at time t = 2 s
(b) when the particle passes through the point (x = l, y = −h)
(c)  when the particle passes through the point (x = l, y = −h)
(d)  when the particle passes through the point (x = 0, y = −h)

Ans. (a, b, c)

Q.20. A man of 60 kg is running on the road and suddenly jumps into a stationary trolly car of mass 120 kg. Then, the trolly car starts moving with velocity 2 ms⁻¹. The velocity of the running man was ___________ m^s−1, when he jumps into the car.             (JEE Main 2022)

Ans. 6

Q.21. The position vector of 1 kg object is  and its velocity
The magnitude of its angular momentum is √x Nm where x is ___________.             (JEE Main 2022)

Ans. 91

Q.22. A bullet of 10 g, moving with velocity v, collides head-on with the stationary bob of a pendulum and recoils with velocity 100 m/s. The length of the pendulum is 0.5 m and mass of the bob is 1 kg. The minimum value of v = ____________ m/s so that the pendulum describes a circle. (Assume the string to be inextensible and g = 10 m/s²)             (JEE Main 2021)

Ans. 400

V' = 5 m/s
m₁ V = m₂ × 5 − m₁ × 100

V = 400 m/s

Q.23. Consider a badminton racket with length scales as shown in the figure.
If the mass of the linear and circular portions of the badminton racket are same (M) and the mass of the threads are negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at, r/2 distance from the end A of the handle will be ................ Mr².             (JEE Main 2021)

Ans. 52

= 52 Mr²
=52.00

Q.24. A body of mass 2 kg moving with a speed of 4 m/s. makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial peed. The speed of the two body centre of mass is x/10 m/s. Then the value of x is ___________.             (JEE Main 2021)

Ans. 25
p_i = p_f
2 × 4 = 2 × 1 + m₂ × v₂
m₂v₂ = 6 ..... (i)
by coefficient of restitution

by (i)
m₂ × 5 = 6
m₂ = 1.2 kg


x = 25

Q.25. The position of the centre of mass of a uniform semi-circular wire of radius 'R' placed in x-y plane with its centre at the origin and the line joining its ends as x-axis is given by Then, the value of | x | is ______________.             (JEE Main 2021)

Ans. 2
Centre of mass of half ring is located at a distance 2R/π from centre of the ring on its axis of symmetry so position of centre of mass in the given question will be
⇒ | x | = 2

Q.26. A rod of mass M and length L is lying on a horizontal frictionless surface. A particle of mass 'm' travelling along the surface hits at one end of the rod with a velocity 'u' in a direction perpendicular to the rod. The collision is completely elastic. After collision, particle comes to rest. The ratio of masses (m/M) is 1/x. The value of 'x' will be ___________             (JEE Main 2021)

Ans. 4
The given situation can be shown as
Before collision,
As the collision is perfectly elastic, therefore momentum is conserved, i.e.
p_initially = p_finally
⇒ mu = Mv ..... (i)
Angular momentum will also be conserved about point O.


∵ Coefficient of restitution,

From Eqs. (ii) and (iii), we get



According to question,
ratio of masses (m/M) = 1x.
Comparing it with Eq. (iv), we get x = 4.

Q.27. The projectile motion of a particle of mass 5 g is shown in the figure.
The initial velocity of the particle is 5√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 __________.             (JEE Main 2021)

Ans. 5






= 50 × 10⁻³
= 5 × 10⁻²

Q.28. A ball of mass 10 kg moving with a velocity 10√3 m/s along the x-axis, hits another ball of mass 20 kg which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along y-axis with a speed of 10 m/s. The second piece starts moving at an angle of 30^∘ with respect to the x-axis. The velocity of the ball moving at 30^∘ with x-axis is x m/s. The configuration of pieces after collision is shown in the figure below. The value of x to the nearest integer is ____________.             (JEE Main 2021)

Ans. 20
Velocity of 10 kg ball

initial total momentum of system

Final total momentum of system

Now by conservation of momentum

⇒ x = 20

Q.29. The disc of mass M with uniform surface mass density σ is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position  where x is _____________. (Round off to the Nearest Integer).
[a is an area as shown in the figure]             (JEE Main 2021)

Ans. 4





= 4R/3π
So the value of x = 4

Q.30. A force  is applied on an intersection point of x = 2 plane and x-axis. The magnitude of torque of this force about a point (2, 3, 4) is ___________. (Round off to the Nearest Integer)             (JEE Main 2021)

Ans. 20

Q.31. A ball of mass 10 kg moving with a velocity 10√3 m s⁻¹ along X-axis, hits another ball of mass 20 kg which is at rest. After collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along Y-axis at a speed of 10 m/s. The second piece starts moving at a speed of 20 m/s at an angle θ (degree) with respect to the X-axis.
The configuration of pieces after collision is shown in the figure.
The value of θ to the nearest integer is ____________.             (JEE Main 2021)

Ans. 30

Conserving momentum along x-axis



∴ θ = 30º

Q.32. Two particles having masses 4 g and 16 g respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is n : 2. The value of n will be ___________.             (JEE Main 2021)

Ans. 1
∵ relation b/w kinetic energy & momentum is



⇒ n = 1

Q.33. Two solids A and B of mass 1 kg and 2 kg respectively are moving with equal linear momentum. The ratio of their kinetic energies (K.E.)A : (K.E.)B will be A/1, so the value of A will be ________.             (JEE Main 2021)

Ans. 2
Given that, M₁/M₂ =1/2
Also, p₁ = p₂ = p
⇒ M₁V₁ = M₂V₂ = p
Also, we know that


⇒ A/1 = 2/1
⇒ ∴ A = 2

Q.34. Angular momentum of a single particle moving with constant speed along circular path :             (JEE Main 2021)
(a) changes in magnitude but remains same in the direction
(b) remains same in magnitude and direction
(c) remains same in magnitude but changes in the direction
(d) is zero

Ans. b

And direction will be upward & remain constant.

Q.35. A body of mass M moving at speed V₀ collides elastically with a mass 'm' at rest. After the collision, the two masses move at angles θ₁ and θ₂ with respect to the initial direction of motion of the body of mass M. The largest possible value of the ratio M/m, for which the angles θ₁ and θ₂ will be equal, is :             (JEE Main 2021)
(a) 4
(b) 1
(c) 3
(d) 2

Ans. c
Given θ₁ = θ₂ = θ
from momentum conservation
in x-direction MV₀ = MV₁ cos_θ + mV₂ cosθ
in y-direction 0 = MV₁ sinθ − mV₂ sinθ
Solving above equations

From energy conservation

Substituting value of V₂ & V₀, we will get

Q.36. Moment of inertia of a square plate of side l about the axis passing through one of the corner and perpendicular to the plane of square plate is given by :             (JEE Main 2021)
(a) Ml²/6
(b) Ml²
(c) Ml²/12
(d) 2/3 Ml²   

Ans. d
According to perpendicular Axis theorem.
Ix + Iy = Iz

= 2Ml²/3    

Q.37. A particle of mass m is suspended from a ceiling through a string of length L. The particle moves in a horizontal circle of radius r such that r = L/√2. The speed of particle will be :             (JEE Main 2021)
(a) √rg
(b) √2rg
(c) 2√rg
(d) √rg/2

Ans. a
r = l/√2
sin⁡θ = r/l = l√2
θ = 45^∘
T sin⁡θ = mv²/r
T cos⁡θ = mg

Q.38. The figure shows two solid discs with radius R and r respectively. If mass per unit area is same for both, what is the rtaio of MI of bigger disc around axis AB (Which is ⊥ to the plane of the disc and passing through its centre) of MI of smaller disc around one of its diameters lying on its plane? Given 'M' is the mass of the larger disc. (MI stands for moment of inertia)             (JEE Main 2021)
(a) R² : r²
(b) 2r⁴ : R⁴
(c) 2R² : r²
(d) 2R⁴ : r⁴    

Ans. d
Ratio of moment of inertia

Q.39.
Choose the correct answer from the options given below:             (JEE Main 2021)
(a) (A)-(ii), (B)-(iii), (C)-(i), (D)-(iv)
(b) (A)-(ii), (B)-(i), (C)-(iii), (D)-(iv)
(c) (A)-(iii), (B)-(iv), (C)-(ii), (D)-(i)
(d) (A)-(iii), (B)-(iv), (C)-(i), (D)-(ii)

Ans. c

Q.40. Two billiard balls of equal mass 30g strike a rigid wall with same speed of 108 kmph (as shown) but at different angles. If the balls get reflected with the same speed then the ratio of the magnitude of impulses imparted to ball 'a' and ball 'b' by the wall along 'X' direction is :             (JEE Main 2021)
(a) 1 : 1
(b) √2 : 1
(c) 2 : 1
(d) 1 : √2

Ans. b
Impulse = change in momentum

Q.41. A bullet of '4 g' mass is fired from a gun of mass 4 kg. If the bullet moves with the muzzle speed of 50 ms⁻¹, the impulse imparted to the gun and velocity of recoil of gun are :             (JEE Main 2021)
(a) 0.2 kg ms⁻¹, 0.1 ms⁻¹
(b) 0.4 kg ms⁻¹, 0.05 ms⁻¹
(c) 0.2 kg ms⁻¹, 0.05 ms−1
(d) 0.4 kg ms⁻¹, 0.1 ms⁻¹  

Ans. c
m_Bullet = 4g, M_Gun = 4 kg
v_Bullet ≃ 50 m/s
Now, P_B = P_g
P_g = m × v_Bullet    

= 0.2 kg m/s
So impulse = 0.2 kg m/s

Q.42. If the Kinetic energy of a moving body becomes four times its initial Kinetic energy, then the percentage change in its momentum will be :             (JEE Main 2021)
(a) 100%
(b) 200%
(c) 300%
(d) 400%

Ans. a
K₂ = 4K₁  

v₂ = 2v₁
P = mv
P₂ = mv₂ = 2mv₁
P₁ = mv₁  

Q.43. An object of mass m₁ collides with another object of mass m₂, which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses m₂ : m₁ is :             (JEE Main 2021)
(a) 1 : 1
(b) 3 : 1
(c) 2 : 1
(d) 1 : 2

Ans. b

Q.44. Two identical blocks A and B each of mass m resting on the smooth horizontal floor are connected by a light spring of natural length L and spring constant K. A third block C of mass m moving with a speed v along the line joining A and B collides with A. The maximum compression in the spring is             (JEE Main 2021)

(a)
(b)
(c)
(d)

Ans. d
From conservation of momentum
mv = mv₁ + mv₁   
V₁ = V/2
And from energy conservation



Then the maximum compression in the spring is

Q.45. A triangular plate is shown. A force   is applied at point P. The torque at point P with respect to point 'O' and 'Q' are :             (JEE Main 2021)
(a) − 15 + 20√3, 15 + 20√3
(b) 15 − 20√3, 15 + 20√3
(c) 15 + 20√3, 15 − 20√3
(d) − 15 − 20√3, 15 − 20√3

Ans. d


Torque about 'O'

Torque about 'Q'

Q.46. A large block of wood of mass M = 5.99 kg is hanging from two long massless cords. A bullet of mass m = 10 g is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their centre of mass rising a vertical distance h = 9.8 cm before the (block + bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is :  
(take g = 9.8 ms^-2)                   (JEE Main 2021)
(a) 831.4 m/s
(b) 811.4 m/s
(c) 841.4 m/s
(d) 821.4 m/s

Ans. a
P_i = 0.01 × u + 0 = P_f = 6 × v
v = 0.01u/6
using energy conservation

Q.47. Four equal masses, m each are placed at the comers of a square of length (l) as shown in the figure. The moment of inertia of the system about an axis passing through A and parallel to DB would be :             (JEE Main 2021)
(a) √3 ml²
(b) 2 ml²
(c) ml²
(d) 3 ml²

Ans. d




Moment of inertia about the axis passing through A :



⇒ I = 3 ml²

Q.48. Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Body 'P' having mass M moving with speed 'u' has head-on collision elastically with another body 'Q' having mass 'm' initially at rest. If m << M, body 'Q' will have a maximum speed equal to '2u' after collision.
Reason R: During elastic collision, the momentum and kinetic energy are both conserved.
In the light of the above statements, choose the most appropriate answer from the options given below :             (JEE Main 2021)
(a) A is correct but R is not correct.
(b) A is not correct but R is 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.

Ans. c
m < < M

For elastic collision → e = 1

u = v₂ − u
v₂ = 2u
In elastic collision kinetic energy & momentum are conserved.