Question

A large spherical planet of radius R, made of a material of density d, has a spherical cavity of radius R/2,with centre of cavity a distance R/2 from the centre other planet. Find the gravitational force one small mass m at the centre of the cavity.

• A. 2RGmd/3
• B. RGmd/3
• C. 2RGmd
• D. 4RGmd/3

Answer 1

The correct option is A 2RGmd/3

$F=m.\frac{GMx}{R^3}$ [where M is the mass of whole body without cavity]

$\begin{array}{c}F=m.\frac{GM}{R^3}.\frac{R}{L}\\ =m\frac{GM}{2R^2}\\ =\frac{GM}{2R^2}.\frac{4}{3}\pi R^3\times d\\ =\frac{2Gmd\pi R}{3}\end{array}$

$\therefore$ Option $A$ is correct answer.