# A tunnel is dug along a diameter of the earth. Find the force on a particle of mass m placed in the tunnel …..

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

$\displaystyle F = \frac{G M_e m x}{R_e ^3}$