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A double star is a system of two stars rotating about their centre of mass only under their mutual gravitational attraction. Let the stars have masses m and 2m and let their separation be l. Their time period of rotation about their centre of mass will be proportional to

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a

l32

b

l

c

m12

d

m−12

answer is A.

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Detailed Solution

r1+r2=l and r1r2=m2m1=21∴r1=2l3Mutual gravitation provides centripetal force. Gm(2m)l2=m(2l3)ω2⇒ml3∝ω2∝1(Timeperiod)2⇒T∝l32 and T∝1/m

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