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Question

A tunnel is dug along a chord of the earth at a perpendicular distance R2 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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C
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Solution

The correct option is C
Net force towards centre of earth
= mg' = mgXR
Thus pressing force N = mgXRR2X
N = mg2= constant and independent of X
tangential force F = ma = mg'
a = =gXRX2R24X
a = gRX2R24
curve is parabolic and at X = R2, a = 0

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