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Q.

A small block of mass m is released from rest from point A inside a smooth hemisphere bowl of radius R, which is fixed on ground such that OA is horizontal. The ratio (x) of magnitude of centripetal force and normal reaction on the block at any point B varies with θ

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a

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b

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c

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d

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answer is A.

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Detailed Solution

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mv2R=N-mg sin θ N=mv2R+mg sin θ

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By energy conservation, mgRsinθ=12mv2

mv2R=2mgsinθ 

N=3mgsinθ 

Ratio=mv2RN=23constant 

x=23

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