Three point masses each of mass m are at the corners of an equilateral triangle of side L. The system rotates about the centre of the triangle with the separation of masses not changing during rotation. If T be the time period of rotation, then

The force of attraction between any two point masses is responsible for providing the necessary centripetal force to a mass to rotate in a circle of radius R From figure,cos⁡30∘=(L/2)R=L2Ror R=L2cos⁡30∘=L3…………..(1)Now,  MRω2=GMM/L2 ………….(2)Substituting the value of R from eq. (1) in eq. (2), we getML3ω2=GM2L2or ω=3GML31/2Therefore, time period T=2πω=2πL33GM1/2∴ T∝L3/2