Q.
A solid sphere of radius $R$ gravitationally attracts a particle placed at $3 R$ form its centre with a force $F _{1}$. Now a spherical cavity of radius $\left(\frac{ R }{2}\right)$ is made in the sphere (as shown in figure) and the force becomes $F _{2}$. The value of $F _{1}: F _{2}$ is

Solution: