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 ?

Explanation

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`