Two concentric spherical shells have masses $M_1$ and $M_2$ and radii $R_1$ and $R_2$ respectively (

Question

Two concentric spherical shells have masses $M_1$ and $M_2$ and radii $R_1$ and $R_2$ respectively ($R_1 < R_2$). What is the force exerted by this system on a particle of mass $m$ if it is placed at a distance $\frac{R_1+R_2}{2}$ from the centre?

Professor PC Thomas Classes · Answer

The point is outside the inner shell but inside the outer shell. By shell theorem, the outer shell exerts zero net force. The inner shell acts as a point mass $M_1$ at the centre. Distance $r = \frac{R_1+R_2}{2}$. Force $F = \frac{GM_1m}{r^2} = \frac{4GM_1m}{(R_1+R_2)^2}$.