Question

The gravitational field of a sphere of mass M and radius R at a distance $2$R from the centre of the sphere is ...... if a cavity of radius R/$3$ is made at the periphery as shown in the 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 $\frac{11GM}{48R^2}$

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

where $M^{\prime }=\frac{M(\frac{R}{3}{)}^3}{R^3}=\frac{M}{27}$

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

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