Three uniform spheres each of mass `m` and diameter `D` are kept in such a way that each touches the other two, then magnitudes of the gravitational force on any one sphere due to the other two is

Options

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

Answer

D

Explanation

Gravitational force on one sphere due to the other two is `F=sqrt(F_(1)^(2)+F_(2)^(2)+2F_(1)F_(2)cos theta)=sqrt(3)F_(1)`
But `F_(1)=(Gm^(2))/(D^(2))rArr F=(sqrt(3)Gm^(2))/(D^(2)) ( :' F_(1)=F_(2))`