Four point mass bodies of masses as shown in Fig. are placed at the vertices of a square `ABCD`, gravitational force on the body at `A`. Given, `G = 6.6 xx 10^(-11) Nm^(2) kg^(-2)`

Explanation

Refer to Fig.

`AB = BC = CD = DA = 0.2 m`
`AC = BD = sqrt((0.2)^(2) + (0.2)^(2)) = 0.2 sqrt(2) m`.
Four particles each of mass `200 g` are located at points `A, B, C` and `D` respectively.
Total work done = gain in `P.E` of the system
`:. W = U_(BA) + (U_(CA) + U_(CB))`
`+ (U_(DA) + U_(DB) + U_(DC))`
`= 4 U_(BA) + 2 U_(DB)`
`[:. U_(BA) = U_(DA) = U_(DC) = U_(CB)` and ` U_(CA) = U_(DB)]`
`= 4 xx [-(Gmm)/(AB)] + 2 [-(Gm xx m)/(BD)]`
or `W = 4 xx [ - (6.67 xx 10^(-11) xx 0.2 xx 0.2)/(0.2)]`
`+ 2 xx [ - (6.67 xx 10^(-11) xx 0.2 xx 0.2)/(0.2 sqrt(2))]`
`= - 5.336 xx 10^(-11) - 1.887 xx 10^(-11)` ltrgt `= - 7.223 xx 10^(-11) J`