In a double star system of two stars of masses m and 2m, rotating about their

Question

In a double star system of two stars of masses m and 2m, rotating about their centre of mass. Their time period of rotation about their centre of mass will be proportional to

Options:

A . r3

B . r

C . m12

D . m−12

Answer: Option D
:
D

r_{2} = \frac{2 m r}{m + 2 m} = \frac{2 r}{3}

In A Double Star System Of Two Stars Of Masses M And 2m, R...

T_{2}^{2} = \frac{4 π^{2} r_{2}^{2}}{G M}

T_{2}^{2} = \frac{32 π^{2} r_{2}^{2}}{27 G M}

T_{2} \propto r^{\frac{3}{2}}

;

T_{2} \propto m^{\frac{- 1}{2}}

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