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Question

A particle is given an initial speed u inside a smooth spherical shell of radius r such that it is just able to complete the circle. Acceleration of the particle at point B is


A
g10
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B
g
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C
g2
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D
3g
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Solution

The correct option is A g10

We know that the critical velocity at the bottom is given by u=5gr
u2=5gr

Using conservation of energy
Δ P.E=Δ K.E
mgr=12mv212mu2

v2=u22gr=5gr2gr=3gr

Tangential acceleration at B is
at=g (downwards)

Centripetal acceleration at B is
ac=v2r=3g

Total acceleration will be
a=a2c+a2t=g10

Hence option A is the correct answer

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