Question

A tunnel is dug along a diameter of the earth. The force on a particle of mass $m$ placed in the tunnel at a distance $x$ from the centre is:

• A. $\frac{G{M}_{e}m}{R^3}x$
• B. $\frac{G{M}_{e}m}{R^2}x$
• C. $\frac{G{M}_{e}m}{R^4}x$
• D. $\frac{G{M}_e}{R^{3}x}$

Answer 1

Answer: (A)

$\frac{G{M}_{e}m}{R^3}x$

Assuming the tunnel doesn't change the gravitational field distribution of earth

Gravitational field at a distance $x$ from the center, $E$ = $\frac{G{M}_e}{R^3}x$

Force on mass $m$ = $mE=\left(\frac{G{M}_{e}m}{R^3}\right)x$