A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The gravitational potential at a point situated at (a/2) distance from the centre, will be:

Question

A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The gravitational potential at a point situated at (a/2) distance from the centre, will be: (A) -(3 G M/a) (B) -(2 G M/a) (C) -(G M/a) (D) -(4 G M/a)

Tardigrade Admin · Accepted Answer

Potential at the given point = Potential at the point due to the shell + Potential due to the particle =-(G M/a)-(2 G M/a)=-(3 G M/a)

Q. A particle of mass $M$ is situated at the centre of a spherical shell of same mass and radius $a$ . The gravitational potential at a point situated at $\frac{a}{2}$ distance from the centre, will be:

$- \frac{3 GM}{a}$

$- \frac{2 GM}{a}$

$- \frac{GM}{a}$

$- \frac{4 GM}{a}$

Potential at the given point $=$ Potential at the point due to the shell $+$ Potential due to the particle
$= - \frac{GM}{a} - \frac{2 GM}{a} = - \frac{3 GM}{a}$

Q. A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The gravitational potential at a point situated at 2a​ distance from the centre, will be:

−a3GM​

−a2GM​

−aGM​

−a4GM​