Three uniform spheres each having a mass M and radius a are kept in such a way that each touches the other two. Find the magnitude of the gravitational force on any of the spheres due to the other two.

Explanation

Given three identical spheres each having a charge q and radius r are kept as shown.

For any external point, sphere behaves like a point charge. So it becomes a triangle having point charges at its corners.
`|vec(F)_(q q)|=(kq^(2))/(4R^(2))`

So, net force `(F)=2. (kq^(2))/(4R^(2)) . "cos "60/2=2. (kq^(2))/(4R^(2)) sqrt(3)/2=sqrt(3)/4 . (kq^(2))/R^(2)`