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A thick walled hollow sphere has outer radius R. It rolls down an inclined plane without slipping and its speed at the bottom is v. If the inclined plane is frictionless and the sphere slides down without rolling, its speed at the bottom is 5v/4. What is the radius of gyration of the sphere?

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a

R2

b

R2

c

3R4

d

3R4

answer is C.

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Detailed Solution

Case 1:mgh=12mv2+12mk2ω2 Case 2:mgh=12m×5v42∴12mk2v2R2+12mv2=12m×25v216⇒k2R2+1=2516 ⇒k=3R4

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A thick walled hollow sphere has outer radius R. It rolls down an inclined plane without slipping and its speed at the bottom is v. If the inclined plane is frictionless and the sphere slides down without rolling, its speed at the bottom is 5v/4. What is the radius of gyration of the sphere?