A sphere of outer radius R having some cavity inside is allowed to roll down on an incline without slipping and it reaches a speed $$v0$$ at the bottom of the incline. The incline is then made smooth by waxing and the sphere is allowed to slide without rolling and now the speed attained is $$(54)v0$$. What is the radius of gyration of the sphere about an axis passing through its centre?

Question

A sphere of outer radius R having some cavity inside is allowed to roll down on an incline without slipping and it reaches a speed $$v0$$ at the bottom of the incline. The incline is then made smooth by waxing and the sphere is allowed to slide without rolling and now the speed attained is $$(54)v0$$. What is the radius of gyration of the sphere about an axis passing through its centre?

Infinity Learn · Accepted Answer

Applying law of CONSERVATION OF ENERGY in the case of $$rolling12mvo2+12I(voR)2$$ $$=$$ mghApplying law of CONSERVATION OF ENERGY in the case of $$sliding12m(54vo)2$$ $$=$$ mghsolve them to get: I $$=$$ $$916mR2now$$ I $$=$$ $$mK2$$, K $$=$$ Im $$=$$ $$34R$$

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