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)pi R^(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^(1)m)/(x^(2))` (or)
`F = (Gm)/(x^(2))((x^(3))/(R^(3))M) = (GMmx)/(R^(3))`