Three uniform spheres each having mass 'm' and radius 'r are kept in such a way that each touches the other. The magnitudeof the gravitational force on any sphere due to the other two is

Three uniform spheres each having mass 'm' and radius 'r are kept in s

1.	Three uniform spheres each having mass 'm' and radius 'r are kept in such a way that each touches the other. The magnitudeof the gravitational force on any sphere due to the other two is
Answer» Solution :Let `F_(1) = F_(2) = F` here `F = (Gm.m.)/((2R)^(2)) = (Gm^(2))/(4R^(2))` `therefore` The resultant gravitational FORCE `F_(R) = 2F COS theta//2` `F_(R)= 2F cos 30^(@) = sqrt(3)F = sqrt(3)(Gm^(2))/((2R)^(2)) = sqrt(3)(Gm^(2))/(4R^(2))`