Consider two configurations of a system of three particles of masses `m`, `2m` and `3m`. The work done by gravity in changing the configuration of the system from figure (i) to figure (ii) is

Options

A. zero
B. `(6 Gm^(2))/(a){1 + (1)/(sqrt(2))}`
C. `(6 Gm^(2))/(a){1 - (1)/(sqrt(2))}`
D. `(6 Gm^(2))/(a){2 - (1)/(sqrt(2))}`

Answer

C

Explanation

`W = - DeltaU = U_(i) - U_(f)`
`= - (Gmm)/(a) [{((1)(2))/(1) +((1) (3))/(1) + ((2)(3))/(sqrt(2))}]`
`-{((1 xx2))/(1) +((1xx3))/(1) + ((2xx3))/(1)}]`
`= (6 GM^(2))/(a)(1- (1)/(sqrt(2)))`