An isolated triple star system consists of two identical stars, each of mass m and a fixed star of mass M. They revolve around the central star in the same circular orbit of radius r. The two orbiting stars are always at opposite ends of a diameter of the orbit. The time period of revolution of each star around the fixed star is equal to:

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4πr3/2G(4M+m)

2πr3/2GM

2πr3/2G(M+m)

4πr3/2G(M+m)

answer is A.

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Detailed Solution

Net gravitational force on any orbiting star provides necessary centripetal force.So GMmr2+Gm24r2=mV2r⇒V=G(4M+m)4r T=2πrV=4πr3/2G(4M+m)

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