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. `2sqrt3Gm^(2)//D^(2)`
C. `sqrt(3GM^(2))//4D^(2)`
D. `sqrt3Gm^(2)//D^(2)`

Answer

d

Explanation

`F_(1)=(Gm^(2))/(D^(2)), F_(2)=(Gm^(2))/(D^(2))`
`F_(1)=F_(2)=F`
`F_(R)=sqrt(F_(1)^(2)+F_(2)^(2)+2F_(1)F_(2)cos 60)`
`=sqrt(F^(2)+F^(2)+2F^(2)xx(1)/(2))`

`=sqrt(3F^(2))=sqrt3F`
`=sqrt3(Gm^(2))/(D^(2))`