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Gravitational force between two point ma...

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 the (a) force on `M` due to `m`, (b) total force on `M`?

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The Gravitational force on m due to M
`F = (GMm)/(r^(2))`
(a) 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 to m, the force doesn.t change.
`therefore F = (GMm)/(r^(2))`
(b) Total force on body of mass M is
`F_(1) = (GM(3m+m))/(r^(2)) = (4GMm)/(r^(2)) = 4F`
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