Gravitational force between two point masses `m` and `M` separated by a distance `r` is `F`. Now if a point mass `3m` is placed next to `m`, what will be that a. force on `M` due to `m`, b total on `M`?

Explanation

(a) If `r` is the distance between two point masses `m` and `M`, then the gravitational force on `m` due
to mass `M` is `F = (GM m)/(r^(2))`
Since, the gravitational force between two point masses is independent of the presence of other masses, so if a point mass `3 m` is placed next to
`m`, the force on `M` due to is, `F = (GM m)/(r^(2))`
(b) Total force on body of mass `M` is,
`F' = (GMxx (m + 3m))/(r^(2)) = (4GM m)/(r^(2)) = 4 F`