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 vary with `x` (distance of the particle from the centre) according to

Options

A.
B.
C.
D.

Answer

B, C

Explanation

Net force towards centre of earth `=mg'=(mgx)//R,`
Normal force `N=mg' sin theta`

Thsu pressing force `N=(mgx)/R R/(2x)`
`N=(mg)/2` is constant and independent of `x`.
Hence `(b)`. Tangential force `F=ma=mg'cos theta`
`Q=g'cos theta=(gx)/R(sqrt(x^(2)-(R^(2))/2))/x`
`a=(gx)/Rsqrt(R^(2)-4x^(2))`.
Curve is parabolic and at `x=R/2,a=0`. hence `(C)`