Question

Gravitational potential due to solid sphere of uniform density and radius $2R$ at a point $P$ is $v_0$. Now a spherical cavity of radius $R$ is made in the sphere as shown in figure. Gravitational potential at $P$ due to sphere with cavity is

• A. $\frac{5}{48}{v}_0$
• B. $\frac{v_0}{5}$
• C. $\frac{v_0}{48}$
• D. $\frac{43}{48}{v}_0$

Answer 1

The correct option is D $\frac{43}{48}{v}_0$

$v_0=\frac{GM}{5R}$
$v_c=\frac{GM}{8\left(6R\right)}=\frac{GM}{48R}$
$v_0-v_c=\frac{GM}{R}(\frac{1}{5}-\frac{1}{48})=\left(\frac{48-5}{240}\right)\frac{GM}{R}$
$=\frac{43}{48}\left(\frac{GM}{5R}\right)$