Question

A solid sphere of mass $M$ and radius $a$ is surrounded by a uniform concentric spherical shell of thickness $2a$ and mass $2M$. The gravitational field at distance $3a$ from the centre will be

• A. $\frac{GM}{9a^2}$
• B. $\frac{2GM}{3a^2}$
• C. $\frac{2GM}{9a^2}$
• D. $\frac{GM}{3a^2}$

Answer 1

The correct option is D $\frac{GM}{3a^2}$

Gravitational field at point $P$, which is at a distance of $3a$ from the center of the sphere.
$E_P=$Gravitational field due to sphere of mass $M+$ Spherical shell of mass $2M$
$\Rightarrow E_P=\frac{GM}{(3a{)}^2}+\frac{G\left(2M\right)}{(3a{)}^2}=\frac{GM}{3a^2}$

For a part on the surface of a spherical uniform charge distribution the whole mass acts as a point mass kept at the centre.
Hence option $\left(C\right)$ is correct.