(a) Three particles of mass `m` each are placed at the three corners of an equilateral triangle of side `a`. Find the work which should be done on this system to increases the sides of the triangle to `2a`,
(b)
Find work done in sending `m` to infinity.

Explanation

(a)

`U_(1)=-(Gm^(2))/axx3=(3Gm^(2))/a`
`U_(2)=-(Gm^(2))/(2a)xx3=-(3Gm^(2))/(2a)`
`W_(1to2)=U_(2)-U_(1)=(3Gm^(2))/(2a)`
(b) `U_(1)=-(GMm)/R`
`U_(oo)=0`
`W_(1tooo)=U_(oo)-U_(1)=(GMm)/R`