(a) A tunnel is dug along a diameter of the earth. Find the force on the a particle of mass `m` placed in the tunnel at a distance `x` from the centre.
(b) 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. Find the force exerted by the wall on a particle of mass `m` when it is at a distance `x` from the centre of the tunnel.