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

Answer

C

Explanation

Gravitational potential at a distance `(a)/(2)` from the centre due to both masses M & M
`V_(1) = (-GM)/((a)/(2))` due to mass M at centre
`V_(2) = (-GM)/(a)` due to spherical shell of radius a
Total potential at point Q due to both masses.
`V_(Q) = V_(1) + V_(2)`
`= ((-GM)/((a)/(2))) + ((-GM)/(a)) = (-3GM)/(a)`