A tunnel is dug along a diameter of the earth. Find the magnitude of the force on a particle of mass

Question

A tunnel is dug along a diameter of the earth. Find the magnitude of the force on a particle of mass $m$ placed in the tunnel at a distance $x$ from the centre. (Given: Mass of earth = $M_e$, Radius = $R$)

Professor PC Thomas Classes · Answer

Inside the earth, $g' = \frac{GM_e}{R^3}x$. Force is $F = mg' = \frac{GM_em}{R^3}x$.