Four bodies each of mass m are placed at the different corners of a square of side a. find the work done on the system to take any one budy to infinity.

Explanation

Initial potential energy of the system
`PE_(1)=PE_(12)+PE_(23)+PE_(34)+PE_(41)+PE_(13)+PE_(24)`

`PE_(1)=-(4GM^(2))/(a)-(2GM^(2))/(asqrt(2))`
After taking any one body (say the mass placed at corner 4) to infinity only three bodies remain `:.` Final potential energy the system is
`PE_(1)=P_(12)+PE_(13)+PE_(23)=-(2GM^(2))/(a)-(GM^(2))/(asqrt(2))`
`W_("ext.")=PE_(f)-PE_(i)=(-(2GM^(2))/(a)-(GM^(2))/(asqrt(2)))-((4GM^(2))/(a)-(2GM^(2))/(asqrt(2)))=(2GM^(2))/(a)+(GM^(2))/(asqrt(2))`.