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

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Infinity Learn · Accepted Answer

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$$,  MRω$$2=GMM/L2$$ ………….$$(2)Substituting$$ the value of R from eq. $$(1) in eq. (2), we $$getML3$$ω$$2=GM2L2or$$ ω$$=3GML31/2Therefore$$, time period $$T=2$$πω$$=2$$$$π$$$$L33GM1/2$$∴ T∝$$L3/2$$

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

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