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Q.

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
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