Question

A uniform solid sphere of mass $M$ and radius $R$ is surrounded symmetrically by a uniform thin spherical shell of mass $\frac{M}{2}$ and radius $2R$. Then gravitational field at a distance $\frac{3R}{2}$ from the centre will be

• A. $\frac{4}{9}\frac{GM}{R^2}$, towards centre
• B. $\frac{3}{2}\frac{GM}{R^2}$, towards centre
• C. $\frac{1}{4}\frac{GM}{R^2}$, towards centre
• D. $\frac{4}{9}\frac{GM}{R^2}$, away from centre

Answer 1

The correct option is A $\frac{4}{9}\frac{GM}{R^2}$, towards centre

The point $P$ is at distance $\frac{3R}{2}$ from the centre.
Since the point $P$ is inside the thin spherical shell.


Therfore at point $P$, gravitational field will be due to the solid sphere of mass $M$ and radius $R$ only.

$\Rightarrow E_g=\frac{GM}{{\left(\frac{3R}{2}\right)}^2}=\frac{4}{9}\frac{GM}{R^2}$

The net gravitational field at $P$ is towards the centre, because gravitational field is attractive in nature and will be towards the solid sphere.