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Question

A hollow vertical cylinder of radius R, with block M on its inner wall, is rotated with angular velocity ω about an axis through its centre. What is the minimum coefficient of static friction between block M and cylinder wall necessary to keep the block suspended on the inside of the cylinder?


A
μ=gRω2
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B
μ=ω2gR
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C
μ=ω2Rg
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D
μ=gω2R
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Solution

The correct option is D μ=gω2R
FBD of block M:

Normal reaction force provides the necessary centripetal force. The force of friction balances the weight of the body.
i.e N=mRω2 & fs=mg
fsμsN
We get, mgμs(mRω2)
μsgRω2
i.e minimum coefficient of friction is gRω2

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