In a solid sphere of mass M and radius R , a spherical cavity of radius (R/2) is made, such that the centre of cavity is at a distance (R/2) from the centre of the sphere. A point mass m is placed inside the cavity, at a distance (R/4) from the centre of the sphere. The gravitational pull between the sphere and the point mass m is

Question

In a solid sphere of mass M and radius R , a spherical cavity of radius (R/2) is made, such that the centre of cavity is at a distance (R/2) from the centre of the sphere. A point mass m is placed inside the cavity, at a distance (R/4) from the centre of the sphere. The gravitational pull between the sphere and the point mass m is (A) (11 G M m/R2) (B) (14 G M m/R2) (C) (G M m/2 R2) (D) (G M m/R2)

Tardigrade Admin · Accepted Answer

The gravitational field inside the cavity is uniform and at the centre of the cavity, it can be calculated as Ecavity-Ec e n t r e=(G M/R3)(R/2)-0=(G M/2 R2) F=(G M m/2 R2)

$\frac{11 GM m}{R ^{2}}$

$\frac{14 GM m}{R ^{2}}$

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

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

The gravitational field inside the cavity is uniform and at the centre of the cavity, it can be calculated as
$E_{c a v i t y} - E_{ce n t re} = \frac{GM}{R ^{3}} \frac{R}{2} - 0 = \frac{GM}{2 R ^{2}}$
$F = \frac{GM m}{2 R ^{2}}$

R211GMm​

R214GMm​

2R2GMm​

R2GMm​

The gravitational field inside the cavity is uniform and at the centre of the cavity, it can be calculated as Ecavity​−Ecentre​=R3GM​2R​−0=2R2GM​ F=2R2GMm​

$\frac{11 GM m}{R ^{2}}$

$\frac{14 GM m}{R ^{2}}$

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

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

The gravitational field inside the cavity is uniform and at the centre of the cavity, it can be calculated as
$E_{c a v i t y} - E_{ce n t re} = \frac{GM}{R ^{3}} \frac{R}{2} - 0 = \frac{GM}{2 R ^{2}}$
$F = \frac{GM m}{2 R ^{2}}$