The mass of a sphere placed on a smooth horizontal surface is distributed $$non-uniformly$$. A horizontal force equal to weight of sphere is applied at a distance 'a' from centre of the sphere for a short time. The sphere is rotated by an angle θ but it behaves as if in stable equilibrium. Find the distance between centre and CG of the sphere:

Question

The mass of a sphere placed on a smooth horizontal surface is distributed $$non-uniformly$$. A horizontal force equal to weight of sphere is applied at a distance 'a' from centre of the sphere for a short time. The sphere is rotated by an angle θ but it behaves as if in stable equilibrium. Find the distance between centre and CG of the sphere:

Infinity Learn · Accepted Answer

The sphere is in stable equilibrium. It will come back to original position after rotation. Rotating Moment $$=$$ Fa. For stable equilibrium, Restoring moment $$=$$ Rotating momentSince $$F=W$$,$$Wa=FaLet$$ O be the centre and C and C' be the positions of CG before and after rotation.$$OC=OC$$′ and C′$$B=a$$........(from$$ $$equation(i)) In ΔOBC′ , OC'$$=$$ C′Bcosec⁡θ$$=acosec$$⁡θ

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