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:

Options

A. `(-3GM)/(a)`
B. `(-4GM)/(a)`
C. `(-2GM)/(a)`
D. `(-GM)/(a)`

Answer

A

Explanation

Here, mass of the particle = M
Mass of the spherical shell = M
Radius of the spherical shell = a
Point P is at a distance `(a)/(2)` from the centre of the shell as shown in the figure.

Gravitational potential at point P due to particle at O is
`V_(1)=-(GM)/((a//2))`
Gravitational potential at point P due to sherical shell is
`V_(2)=-(GM)/(a)`
Hence, total gravitational potential at the point P is,
`V=V_(1)+V_(2)`
`=-(GM)/((a//2))+(-(GM)/(a))`
`=-(2GM)/(a)-(GM)/(a)=-(3GM)/(a)`