Question

In a solid sphere of mass $M$ and radius $R$ , a spherical cavity of radius $\frac{R}{2}$ is made, such that the centre of cavity is at a distance $\frac{R}{2}$ from the centre of the sphere. A point mass $m$ is placed inside the cavity, at a distance $\frac{R}{4}$ from the centre of the sphere. The gravitational pull between the sphere and the point mass $m$ is

• A. $\frac{11 G M m}{R^{2}}$
• B. $\frac{14 G M m}{R^{2}}$
• C. $\frac{G M m}{2 R^{2}}$
• D. $\frac{G M m}{R^{2}}$

Answer 1

Answer: (C)

The gravitational field inside the cavity is uniform and at the centre of the cavity, it can be calculated as
$E_{cavity}-E_{c e n t r e}=\frac{G M}{R^{3}}\frac{R}{2}-0=\frac{G M}{2 R^{2}}$
$F=\frac{G M m}{2 R^{2}}$