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 center- The collision is instantaneous and completely inelastic- Which of the following is-are correct -A- Total linear momentum of the system is not conservedB- Total angular momentum about center of mass of the system remains conservedC- The sphere gets finite angular velocity immediately after collisionD- The sphere moves with finite speed immediately after collision

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Newton's Second Law: Rotatory Version

A hollow sphe...

Question

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 center. The collision is instantaneous and completely inelastic. Which of the following is/are correct ?

Total linear momentum of the system is not conserved

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Total angular momentum about center of mass of the system remains conserved

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The sphere gets finite angular velocity immediately after collision

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The sphere moves with finite speed immediately after collision

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Solution

The correct options are
A Total linear momentum of the system is not conserved
C
The sphere gets finite angular velocity immediately after collision

D
The sphere moves with finite speed immediately after collision

Impulse due to normal reaction is finite. So friction force gives finite impulse. Therefore frictional torque causes a finite angular impulse about center of mass of system so angular momentum about center of mass of system will change. All other options are correct.

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