Q: A tunnel is dug along a diameter of the earth. Find the force on a particle of mass m placed in the tunnel at a distance x from the centre
(a) $ \displaystyle \frac{G M_e m x}{R_e^3} $
(b) $ \displaystyle \frac{G M_e m}{3 R_e^2} $
(c) $ \displaystyle \frac{G M_e m}{2 R_e^2} $
(d) $ \displaystyle \frac{2 G M_e m}{3 R_e^2} $
Ans: (a)
Gravitational Field Strength at a distance x from the centre is
$ \displaystyle E = \frac{G M_e x}{R_e ^3} $
Force on a particle of mass m is
F = m E
$ \displaystyle F = \frac{G M_e m x}{R_e ^3} $