Question

A solid sphere of mass $m$ and radius $r$ is placed inside a hollow thin spherical shell of mass $M$ and radius $R$ as shown in figure. A particle of mass $m^{{}^{\prime }}$ is placed on the line joining the two centres at a distance $x$ from the point of contact of the sphere and shell. Find the magnitude of force $($gravitational$)$ on this particle when $2r<x<2R$.

• A. $\frac{Gm{m}^{{}^{\prime }}}{x^2}$
• B. $\frac{Gm{m}^{{}^{\prime }}}{(x-r{)}^2}$
• C. $\frac{Gm{m}^{{}^{\prime }}}{x^2}+\frac{GmM}{x^2}$
• D. $\frac{Gm{m}^{{}^{\prime }}}{(x-r{)}^2}+\frac{GMm}{(x-R{)}^2}$

Answer 1

The correct option is B $\frac{Gm{m}^{{}^{\prime }}}{(x-r{)}^2}$

The shell of mass M exerts no force as its gravitational field inside is zero. So the force on the particle will come due to solid sphere.
thus, $F=\frac{Gm{m}^{\prime }}{(x-r{)}^2}$