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Q.

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?

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a

25R

b

23R

c

(45)R

d

(34)R

answer is D.

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Detailed Solution

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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