A spherical hollow is made on a lead sphere of radius R such that its surface touches the outside
surface of the lead sphere and passes through its centre. The mass of the lead sphere before hollowing was M. What
is the force of attraction that this sphere would exert on a particle of mass m which lies at a distance d from the centre
of the lead sphere on the straight line joining the centres of the sphere and the hollow.

Explanation

As the point mass m is outside the lead sphere we can assume its mass to be concentrated at the centre.
To calculate the force of attraction on the point mass m we should calculate the force due to the solid sphere and
subtract from this the force which the mass of the hollowed sphere would have exerted on m, i.e.,
`F=("GmM")/(d^(2))-("GmM".)/(y^(2))`

But from figure `y=[d-((R)/(2))]`
and as M = `((4)/(3))piR^(3)P,M.=((4)/(3))pi((R)/(2))^(3)P=((M)/(8))`
so, `F=("GMm")/(d^(2))-("Gm"(M//8))/([d-(R//2)]^(2))=("GMm")/(d^(2))[1-(1)/(8[1-(R//2d)]^(2))]`