Three, point masses each of mass ' m ' are kept at the corners of an equilateral triangle of side ' L '. The system rotates about the center of the triangle without any change in the separation of masses during rotation. The period of rotation is directly proportional to

Step-by-step solution

Consider mass m at A . The forces exerted on it by the other two masses are given by F ₁= G m ^2 ~L ^2 = F ₂ The angel between the two forces is 60^ . Hence the resultant force The angel between the two forces is 60^ . Hence the resultant force aligned & F = F ₁^2+ F ₁^2+2 ~F ₁^2 60^ = 3 ~F ₁ & ~F = 3 G m ^2 ~L ^2 aligned radius r= L 3 For uniform circular motion, the gravitational force provides the centripetal force. aligned & mr ^2= F & m L 3 ^2= 3 G m ^2 ~L ^2 & ^2=3 G m L ^3 aligned aligned & = (3 G m L ^3 )^