HARD
JEE Main/Advance
IMPORTANT
Earn 100

A uniform rod having mass m1 and length L lies on a smooth horizontal surface. A particle of mass m2 moving with speed u on the horizontal surface strikes the free rod perpendicularly at an end and it sticks to the rod.

a Calculate the velocity of the centre of mass C of the system constituting the rod plus the particle.

b Calculate the velocity of the particle with respect to C before the collision.

c Calculate the velocity of the rod with respect to C before the collision.

d Calculate the angular momentum of the particle and of the rod about the centre of mass C before the collision.

e Calculate the moment of inertia of the rod plus particle about the vertical axis through the centre of mass C after the collision.

f Calculate the velocity of the centre of mass C and the angular velocity of the system about the centre of mass after the collision.

Important Questions on Centre of Mass, Momentum and Collisions

EASY
JEE Main/Advance
IMPORTANT
A uniform sphere is placed is placed on a smooth horizontal surface and a horizontal force F is supplied on it a t a distance h above the centre. The acceleration of the centre of mass of the sphere.
EASY
JEE Main/Advance
IMPORTANT
A ball moves horizontally in a closed box making several collisions with the walls. The box is kept on a smooth horizontal surface. During the motion of the ball, the velocity of the centre of mass:
EASY
JEE Main/Advance
IMPORTANT

A block of mass M with a semicircular track of radius R rests on a horizontal frictionless surface. A uniform cylinder of radius r and mass m is released from rest from the top point A. The cylinder slips on the semicircular frictionless track. The distance travelled by the block when the cylinder reaches the point B is:

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MEDIUM
JEE Main/Advance
IMPORTANT

A block of mass M with a semicircular track of radius R rests on a horizontal frictionless surface. A uniform cylinder of radius r and mass m is released from rest from the top point A. The cylinder slips on the semicircular frictionless track.

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The velocity of the block when the cylinder reaches point (B) is:
MEDIUM
JEE Main/Advance
IMPORTANT
A uniform thin rod of mass M and Length L is standing vertically along the y-axis on a smooth horizontal surface with its lower end at the origin (0,0). A slight disturbance at t=0 causes the lower end to slip on the smooth surface along the positive x-axis and the rod starts falling. The acceleration vector of centre of mass of the rod during its fall is: [R is reaction from surface]
EASY
JEE Main/Advance
IMPORTANT

In a vertical plane inside a smooth hollow thin tube a block of same mass as that of tube is released as shown in the figure. When it is slightly disturbed it moves towards right. By the time the block reaches the right end of the tube, displacement of the tube will be (where R is mean radius of tube). Assume that the tube remains in vertical plane.

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EASY
JEE Main/Advance
IMPORTANT

Two men A and B are standing on a plank. B is at the middle of the plank and A is at the left end of the plank. The bottom surface of the plank is smooth. The system is initially at rest and masses are as shown in the figure. A and B start moving such that the position of B remains fixed with respect to ground and A meets B. Then the point where A meets B is located at

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HARD
JEE Main/Advance
IMPORTANT

A small sphere of radius R is held against the inner surface of a larger sphere of radius 6R. The masses of large and small spheres are 4M and M respectively. This arrangement is placed on a horizontal table as shown. There is no friction between any surfaces of contact. The small sphere is now released. The coordinates of the centre of the large sphere when the smaller sphere reaches the other extreme position is :

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