Question

A uniform metal sphere of radius a and mass M is surrounded by a thin uniform spherical shell of equal mass and radius 4a (figure 11-E2). The centre of th shell on the surface of the inner sphere. Find th egravitational field at the points $P_1$ and $P_2$ shown in the figure.

Answer 1

At$P_1$ Gravitational field due to sphere M
$=\frac{GM}{(3a+a{)}^2}=\frac{GM}{16a^2}$
At $P_2$ Gravitational field is due to sphere and shell
$=\frac{GM}{(a+4a+a{)}^2}\frac{GM}{(4a+a{)}^2}=\frac{GM}{36a^2}+\frac{GM}{25a^2}=\frac{GM}{a^2}(\frac{1}{36}+\frac{1}{25})=\frac{GM}{a^2}\left(\frac{25+36}{900}\right)=\left(\frac{61}{900}\right)\frac{GM}{a^2}$