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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a
4πr3/2G(4M+m)
b
2πr3/2GM
c
2πr3/2G(M+m)
d
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)
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: