A spherical cavity is made inside a sphere of density, `d`. Its centre lies at a distance `l`, from the centre of sphere, show that the gravitational strength, `I`, of the field inside the cavity is `= (4//3) xx pi Gld`.

Explanation

Let centre `C` of the cavity be lying on the surface of a solid sphere of radius `OC = l` and density of earth `= d`. Fig.

Mass of the shaded sphere, `M = (4)/(3) pi l^(3) d`
Gravitational intensity inside the cavity (i.e., at point `C`) is
`I = (GM)/(l^(2)) = (G)/(l^(2)) xx (4)/(3) pi l^(3) d = (4)/(3) pi G ld`