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Question

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?

A
R2
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B
R2
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C
3R4
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D
3R4
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Solution

The correct option is C 3R4
Case I: mgh=12mv2+12mk2ω2
V=ωR
mgh=12mv2+12mk2v2R2

Case II: mgh=12m×(5v4)2 12mk2v2R2+12mv2=12m×25v216 K2R2+1=2516k=3R4

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