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

Explanation

Mass of earth `M=4/3 piR^3 rho`
Mass of imaginary sphere,
having radius x,
`M_1=4/3 pi x^3 rho` (or)`M^1/M=x^3/R^3`
`therefore` Gravitational force on .m. due to `M_1`
`F=(GM^1m)/x^2` (or) `F=(Gm)/x^2 (x^3/R^3 M)="GMmx"/R^3`