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Question

A tunnel is dug along a chord of the earth at a perpendicular distance R/2 from the earth's centre. The wall of the tunnel may be assumed to be frictionless. A particle is released from one end of the tunnel. The pressing force by the particle on the wall and the acceleration of the particle varies with x (distance of the particle from the centre) according to


A

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B

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C

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D

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Solution

The correct option is B


Net force towards centre of earth = mg' = mgxR

Normal force N = mg'sinθ

Thus pressing Force N = mgxRR2x

N= Mg2 constant and independent of x.

Hence (B) Tangential force F=ma=mg'cosθ

Q=g'cosθ=gxR24x2rx

α = gx R24x2


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