Two concentric spherical shells have masses M1, M2 and radii R1, R2….

Q: Two concentric spherical shells have masses M₁, M₂ and radii R₁, R₂ (R₁ < R₂). The force exerted by this system on a particle of mass m if it is placed at a distance (R₁ + R₂)/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 = E₁ + E₂

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

F = m₁ E