A spherical cavity of radius(R )/(2)is removed from a solid sphere of radius R as shown in fig. The sphere is placed on a rough horizontal surface as shown. The sphere is given a gentle push. Friction is large enough to prevent slippage. Prove that the sphere perform SHM and find the time period.

A spherical cavity of radius(R )/(2)is removed from a solid sphere of

1.	A spherical cavity of radius(R )/(2)is removed from a solid sphere of radius R as shown in fig. The sphere is placed on a rough horizontal surface as shown. The sphere is given a gentle push. Friction is large enough to prevent slippage. Prove that the sphere perform SHM and find the time period.
Answer» ANSWER :`T=2 PI SQRT((177R)/(10G))`