Question

The gravitational field of a sphere of mass $M$ and radius $R$ at a distance $2R$ from the centre of the sphere is ............... if a cavity of radius $R/3$ is made at the periphery as shown in figure.

• A. $\frac{11GM}{48R^2}$
• B. $\frac{9GM}{48R^2}$
• C. $\frac{7GM}{48R^2}$
• D. none of these

Answer 1

The correct option is A $\frac{11GM}{48R^2}$

$E_g=\frac{GM}{(2R{)}^2}-\frac{G{M}^{\prime }}{{(R+\frac{R}{3})}^2}$ where M'

$=\frac{M{\left(\frac{R}{3}\right)}^3}{R^3}=\frac{M}{27}$

$=\frac{GM}{R^2}[\frac{1}{4}-\frac{9}{16\times 27}]$

$=\frac{GM}{R^{2}4}\left[\frac{11}{12}\right]=\frac{11GM}{48R^2}$