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

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) ( GMm / x 2) (B) ( GMm x/R3) (C) (G(M+m)/x2) (D) Zero

Tardigrade Admin · Accepted Answer

The gravitational force on the point mass

m

due to uniform sphere

= \frac{GM 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.

Q. 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

$\frac{GM m}{x ^{2}}$

$\frac{GM m x}{R ^{3}}$

$\frac{G ( M + m )}{x ^{2}}$

Zero

Q. A uniform sphere of mass M and radius R is surrounded by a concentric spherical shell of same mass but radius 2R. 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

x2GMm​

R3GMmx​

x2G(M+m)​

Zero

Q. 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

$\frac{GM m}{x ^{2}}$

$\frac{GM m x}{R ^{3}}$

$\frac{G ( M + m )}{x ^{2}}$