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Question

A particle is placed at rest inside a hollow hemisphere of radius R. The coeffieient of friction between the particle and the hemisphere is μ=13. The maximum height up to which the particle can remain stationary is:

A
R2
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B
(132)R
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C
32R
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D
3R2
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Solution

The correct option is B (132)R
Let the body is at θ from the vertical.
Therefore force in radial direction would be mgcosθ
Force along tangential direction would be a part of force due to gravity (downwards) and friction force (upwards) , mgsinθ,μN=μmgcosθ respectively.
So body will remain stationary when mgsinθμmgcosθ
For maximum height: mgsinθ=μmgcosθtanθ=1/3&θ=30
So maximum height: R(Rcosθ)=R(1cosθ)=R(132)
339069_236300_ans_6c2611570b764b92a557f11001e3ac0b.png

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