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Question

A particle of mass, m, oscillates along a semi-circular path ACB inside a fixed smooth spherical shell of radius, R. It is released from point A. If at any instant KE of the particle is K, then the force applied by particle on the shell at this instant is:

78395_baeecbc9d5334b8dbd5c0d189ff54d4f.png

A
KR
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B
2KR
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C
3KR
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D
K2R
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Solution

The correct option is B 3KR
From the conservation of energy principle:
mgRsinθ=12mv2
And, from the equation of motion:
2mgsinθ=mv2R

So, using the given condition:
mgRsinθ=K
and, mgsinθ=KR

Force applied by the particle on the shell:
N=mv2R+mgsinθ
or, N=2mgsinθ+mgsinθ
or, N=3mgsinθ
or, N=3KR

135475_78395_ans_a430c98f5a3f490eba72cdbe51531998.png

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