Inside a uniform sphere of density `rho` there is a spherical cavity whose centre is at a distance `l` from the centre of the sphere. Find the strength G of the gravitational field inside the cavity.

Explanation

Treating the cavity as negative mass of density `-rho` in a uniform sphere density `+rho` and using the superposition principle, the sought field strength is:
`vecG=vecG_1+vecG_2`
or `vecG=-4/3pilambdarhovecr_++ -4/3lambdapi(-rho)vecr_-`
(where `vecr_+` and `vecr_-` are the position vectors of an orbitrary point P inside the cavity with respect to centre of sphere and cavity respectively.)
Thus `vecG=-4/3pigammarho(vecr_(+)-vecr_(-))=-4/3pigammarhovecl`