Question

A uniform sphere of mass $M$ and radius $R$ is surrounded by a concentric spherical shell of same mass but radius $2 R$. A point mass $m$ is kept at a distance $x(>R)$ in the region bounded by spheres as shown in the figure. The net gravitational force on the particle is

• A. $\frac{ GMm }{ x ^{2}}$
• B. $\frac{ GMm x}{R^{3}}$
• C. $\frac{G(M+m)}{x^{2}}$
• D. Zero

Answer 1

Answer: (A)

The gravitational force on the point mass $m$ due to uniform sphere $=\frac{G M m}{x^{2}}$.
The gravitational force on the point mass due to the outer spherical shell is zero because gravitational force of attraction on a point mass due to various rejoins of the spherical shell cancels each other completely as their vector sum is zero.