Three identical stars, each of mass `M`, from an equilateral triangle (stars are positioned at the corners) that rotates around the centre of the triangle. The system is isolated and edge length of the triangle is `L`. The amount of work done, that is required ot dismantle the system, is:

Options

A. `(3GM^(2))/(L)`
B. `3/2 (GM^(2))/L`
C. `3/4 (GM^(2))/L`
D. `(GM^(2))/(2L)`

Answer

B

Explanation

Stars move around COM. Distance of each star form COM is `2/3xxLcos 30^(@)=L/(sqrt(3))`
Force on each star `M` due to the other two
`2.(G.M.M)/(L^(2))cos30^(@)=sqrt(3) (GM^(2))/(L^(2))`
This acts as centripetal force.
Therefore, `sqrt(3) (GM^(2))/(L^(2))=(mv^(2))/((L//sqrt(3))implies V=sqrt((GM)/L)`
To dismantle the system, energy equal to total energy of the system must be provided.
i.e. `3xx1/2MV^(2)+(3xx(GM^(2))/L)=-3/2 (GM^(2))/L`