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. ` -(2GM)/( a)`
C. ` - (GM)/(a)`
D. ` -(4GM)/(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 figure. Gravitational potential at point P due to particle at O is
`V_1 =- (GM)/((a //2))`
Gravitational potential at point P due to spherical 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)`