A double star consists of two stars having masses m and 2m. The distance between their centres is r. They revolve in circular orbits keeping a constant radius. Then choose the correct statement(s):
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a
The heavier star revolves in a circle of radius r3
b
Both the stars revolve with the same period
c
The period of revolution of each star is 2πr3/22Gm3
d
The period of revolution of each star is 2πr3/23Gm
answer is A.
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Detailed Solution
r1+r2=r and r1r2=m2m1=21⇒r1=2r3small star and r2=r3big starGravitational force provides centripetal force.⇒G2mmr2=m2r3ω2⇒ω=3Gmr3⇒T=2πω=2πr33Gm