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_(i)=PE_(12)+PE_(23)+PE_(34)+PE_(41)+PE_(13)+PE_(24)`
`PE_(i)= - (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_(f)=P_(12)+PE_(13)+PE_(23)= - (2GM^(2))/a - (GM^(2))/(a sqrt(2))`
`W_("ext")=PE_(f)-PE_(i)=(-(2GM^(2))/a-(GM^(2))/(a sqrt(2)))-(-(4GM^(2))/a-(2GM^(2))/(asqrt(2)))=(2GM^(2))/a+(GM^(2))/(a sqrt(2))`