Four point masses each of mass m are placed at corners of square of side d and a mass M is placed at centre. The gravitational potential energy of system is

Options

A. `-(Gm)/d[(4+sqrt(2))m+4sqrt(2)M]`
B. `-(Gm)/d [(4+sqrt(2))M+4sqrt(2)m]`
C. `-(Gm)/d[3m^(2)+4sqrt(2)M]`
D. `-(Gm)/d [6m^(2)+4sqrt(2)M]`

Answer

A

Explanation

`PE = -((4Gm^(2))/d+(2Gm^(2))/(sqrt(2d))+(4GmM)/(d//sqrt(2)))=-(Gm)/d[4sqrt(2)M+m(4+sqrt(2))]`