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.

Options

A. `(GM^(2))/(4r^(2))`
B. `(2GM^(2))/(r^(2))`
C. `(2GM^(2))/(4r^(2))`
D. `(sqrt(3)GM^(2))/(4r^(2))`

Explanation

`vecF=vecF_(1)=vecF_(2)`
As `|vecF_(1)|=|vecF_(2)|`
`:. |vecF|=2F_(1)cos30^@`
`=2(GM^(2))/((2r)^(2))(sqr(3))/2=(sqrt(3))/4(GM^(2))/(r^(2))`