Question

A uniform metal sphere of radius $R$ and mass m is surrounded by a thin uniform spherical shell of same mass and radius $4R$ The centre of the shell $C$ falls on the surface of the inner sphere. Find the gravitational fields at points A and B.

Answer 1

(i) At point A, field strength due to shell will be zero.
Net field is only due to metal sphere. Distance between centre of metal sphere and point A is 4R.
$\therefore$ $E_A=\frac{G\left(m\right)}{{\left(4R\right)}^2}=\frac{Gm}{16R^2}$
(ii) At point B, net field is due to both, due to shell and due to metal sphere.
$\therefore$ $E_B=\frac{Gm}{{\left(5R\right)}^2}+\frac{Gm}{{\left(6R\right)}^2}=\frac{61Gm}{900R^2}$