Q: Two concentric spherical shells have masses *M*_{1}, *M*_{2} and radii *R*_{1}, *R*_{2} (*R*_{1} < *R*_{2}). The force exerted by this system on a particle of mass *m* if it is placed at a distance (*R*_{1} + *R*_{2})/2 from the centre

(a) $\displaystyle \frac{2 G M_1 m}{(R_1 + R_2)^2} $

(b) $ \displaystyle \frac{ G M_1 m}{(R_1 + R_2)^2} $

(c) $\displaystyle \frac{2 G M_1 m}{2(R_1 + R_2)^2} $

(d) $ \displaystyle \frac{4 G M_1 m}{(R_1 + R_2)^2} $

Ans: (d)

E = E_{1} + E_{2}

$ \displaystyle = \frac{GM_1}{((R_1 + R_2)/2)^2} + 0 $

F = m_{1} E