Two balls having linear momenta p → 1 = p i ^ and p → 2 = - p i ^ , undergo a collision in free space. There is no external force acting on the balls. Let p → 1 ' and p → 2 ' be their final momenta. The following option (s) is (are) not allowed for any non-zero value of p , a 1 , a 2 , b 1 , b 2 , c 1 and c 2 .

p 1 ' → = a 1 i ^ + b 1 j ^ + c 1 k ^ , p 2 ' → = a 2 i ^ + b 2 j ^

p 1 ' → = c 1 k ^ , p 2 ' → = c 2 k ^

p 1 ' → = a 1 i ^ + b 1 j ^ + c 1 k ^ , p 2 ' → = a 2 i ^ + b 2 j ^ - c 2 k ^

p 1 ' → = a 1 i ^ + b 1 j ^ , p 2 ' → = a 2 i ^ + b 1 j ^

HARD

JEE Main/Advance

IMPORTANT

Earn 100

A projectile is thrown horizontally from top of a tower of height $20 m$ with a velocity $10 m / \sec .$ It strikes the smooth ground whose co-efficient of restitution is $0.5 . [g = 10 m / s^{2}]$ (neglect friction):

66.67% studentsanswered this correctly

Important Questions on Centre of Mass, Momentum and Collisions

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise - 2>Q 73

Two balls

A and B

moving in the same direction collide. The mass of

B

p

times that of

A .

Before the collision the velocity of

A

was

q

times that of

B .

After the collision

A

comes to rest. If

e

be the coefficient of restitution then which of the following conclusion/s is/are correct ?

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise - 2>Q 78

A particle is attached to the lower end of a uniform rod which is hinged at its other end as shown in the figure. The minimum speed given to the particle so that the rod performs circular motion in a vertical plane will be [length of the rod is $l$ , consider masses of both rod and particle to be same]

Question Image

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise - 2>Q 79

A rod of negligible mass and length $l$ is pivoted at the point $\frac{l}{4}$ distance from the left end as shown. A particle of mass $m$ is fixed to its left end and another particle of mass $2 m$ is fixed to the right end. If the system is released from rest and after some time becomes vertical, the speed $v$ of the two masses and angular velocity at that instant is

Question Image

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise - 2>Q 80

Two identical balls $A$ and $B$ of mass $m$ each is placed on a fixed wedge as shown in the figure. The ball $B$ is kept at rest and it is released just before two balls collide. The ball $A$ rolls down without slipping on an inclined plane and collides elastically with the ball $B$ . The kinetic energy of the ball $A$ just after the collision with the ball $B$ is (Neglect friction between $A$ and $B$ , also neglect the radius of the balls)

Question Image

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise - 2>Q 81

Consider two point masses

m_{1}

and

m_{2}

connected by a light rigid rod of length

r_{0}

. The moment of inertia of the system about an axis passing through their centre of mass and perpendicular to the rigid rod is given by

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise - 3>Q 1

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 N s

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^{- \frac{t}{τ}}

, where

v_{0}

is a constant and

τ = 4 s

. The displacement of the block, in metres, at

t = τ

is __________. Take

e^{- 1} = 0.37

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise - 3>Q 2

Statement-1: In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.

Statement-2: In an elastic collision, the linear momentum of the system is conserved.

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 9 - Centre of Mass, Momentum and Collisions>Exercise - 3>Q 3

Two balls having linear momenta

{\vec{p}}_{1} = p \hat{i}

and

{\vec{p}}_{2} = - p \hat{i}

, undergo a collision in free space. There is no external force acting on the balls. Let

{\vec{p}}_{1}^{'}

and

{\vec{p}}_{2}^{'}

be their final momenta. The following option (s) is (are) not allowed for any non-zero value of

p, a_{1}, a_{2}, b_{1}, b_{2}, c_{1}

and

c_{2}

A projectile is thrown horizontally from top of a tower of height 20 m with a velocity 10 m/sec. It strikes the smooth ground whose co-efficient of restitution is 0.5. [g = 10 m/s2] (neglect friction):

Important Questions on Centre of Mass, Momentum and Collisions

Learn and Prepare for any exam you want !

A projectile is thrown horizontally from top of a tower of height $20 m$ with a velocity $10 m / \sec .$ It strikes the smooth ground whose co-efficient of restitution is $0.5 . [g = 10 m / s^{2}]$ (neglect friction):