A system consists three particles, each of mass `M` lying on the corners of an equilateral triangle of side `2l`. If the length of each side of the triangle is decreased to `l`, without the gain in kinetic energy of the particles, the work done by an external agent is given by

Options

A. `(-3GM^(2))/(2l)`
B. `(3GM^(2))/(2l)`
C. `(GM^(2))/(l)`
D. `(-1.5GM)/(l)`

Explanation

`u_(i)=-(3GM^(2))/(2l)`
`U_(f)=-(3GM^(2))/(l)`
`DeltaW_(conservative)=DeltaW_(system)=-(U_(t)-U_(i))=-[-(3GM^(2))/(l)+(3GM^(2))/(2l)]=(3GM^(2))/(2l)`