A hollow sphere of radius R rests on a horizontal surface of finite coefficient of friction. A point object of mass m moved horizontally and hits the sphere at a height of R/2 above its centre. The collision is instantaneous and completely inelastic. Which of the following is/are correct?

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The sphere moves with finite speed immediately after collision.

Total angular momentum about centre of mass of the system remain conserved.

The sphere gets finite angular velocity immediately after collision.

Total linear momentum of the system is not conserved.

answer is A, C, D.

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Detailed Solution

Impulse due to normal reaction is finite. So, the friction force gives finite impulse.
Therefore, the frictional torque causes a finite angular impulse about centre of mass of system so, the angular momentum about centre of mass of system changes. Hence, all other options are correct.

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