A particle of mass M is placed at the centre of a uniform spherical shell of equal mass and radius a. Find the gravitational potential at a point P at a distance `a/2` from the centre.

Options

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

Answer

A

Explanation

Here, mass of the particle `=M` Mass of the spherical shell `=M` Radius of the spherical shell `=R` Let `O` be centre of spherical shell. Gravitational potential at point `P` due to particle at `O` is
`V_(1)=-(GM)/((R//2))`

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