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

D

Explanation

Let mass of the earth is `M_(e)` and mass of object is m.
Force on object at `A=((GM_(e)m)/(R^(3))r)` towards centre
Force ono object along the tunnel `=((GM_(e))/(R^(3))r)(sqrt(r^(2)-(R^(2))/(4)))/(r)`
Acceleration of object along the tunnel `=((GM_(e))/(R^(3)))sqrt(r^(2)-(R^(2))/(4))`