CENTRE OF MASS

A mass of man m standing on a block of mass M. The system is at rest. The man moves relative in x direction to the block with velocity v' and then stops. Velocity of centre of mass will be :

• v'

• 0

• mv′/ M+m

• None of these

Two objects P and Q initially at rest move towards each other under a mutual force of attraction. At the instant when the velocity of P is V and that of Q is 2v the velocity of the centre of mass of the system is:

• V

• 2V

• ZERO

• 4V

A ball kept in a closed container moves in it making collision with the walls. The container is on a smooth surface. The velocity of the centre of mass of:

• the ball remains fixed.

• ball relative to container remains the same.

• container remains fixed.

• ball container and ball remains fixed.

Two unequal masses are tied together with a compressed spring. When the cord is burnt with a matchstick releasing the spring; the two masses fly apart with equal :

• Momentum

• Acceleration

• Speed

• Kinetic energy

A cricket bat is cut at the location of its centre of mass as shown. Then,

• the two pieces will have the same mass

• the bottom piece will have larger mass

• the handle piece will have larger mass

• mass of handle piece is double the mass of bottom piece

Choose the correct statement.

(A) The position of centre of mass of a system is dependent on the choice of co-ordinate system.

(B) Newton's second law of motion is applicable to the centre of mass of the system.

(C) When no external force acts on a body, the acceleration of centre of mass is zero.

(D) Internal forces can change the state of centre of mass.

• Both A and B are correct

• Both B and C are wrong

• Both A and C are wrong

• Both A and D are wrong

Can the centre of mass of a body be at a point outside the body?

• Yes

• No

If all the particles of a system lie in X-Y plane, is it necessary that the centre of mass be in X-Y plane?

• Yes

• No

If all the particle of a system lie in a cube, is it necessary that the centre of mass be in the cube?

• Yes

• No

Two balls are thrown simultaneously in air. The acceleration of the centre of mass of the two balls while in air:

• depends on the direction of the motion of the balls

• depends on the masses of the two balls

• depends on the speeds of the two balls

• is equal to g