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

Answer 1

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

Draw a labelled diagram.

Find the gravitational field at distance $3a$.
Gravitational field due to solid sphere of radius a at a distance,
$r=3a,i.e.,(r>R)$ is

$E_1=\frac{GM}{r^2}=\frac{GM}{(3a{)}^2}=\frac{GM}{9a^2}$

Similarly, gravitational field due to spherical shell at a distance,$r=3a,$

$E_2=\frac{GM}{R^2}=\frac{G\left(2M\right)}{(3a{)}^2}=\frac{2GM}{9a^2}$

Both fields are attractive in nature, so direction will be same.
Net field, $E_{\text{net}}=\frac{GM}{3a^2}$

Final Answer: (b)