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.
• B.
• C.
• D.

Answer 1

The correct option is B

Net force towards centre of earth = mg' = $\frac{mgx}{R}$

Normal force N = mg'sin$\theta$

Thus pressing Force N = $\frac{mgx}{R}$$\frac{R}{2x}$

N= $\frac{Mg}{2}$ constant and independent of x.

Hence (B) Tangential force F=ma=mg'cos$\theta$

Q=g'cos$\theta$=$\frac{gx\sqrt{\frac{R^2}{4}}-x^2}{rx}$

$\alpha$ = $\frac{g}{x}$ $\sqrt{R^2-4x^2}$