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Question: A double star is a system of two stars rotating about their centre of mass only under their mutual g...

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

(Double star)

A

l2/3l^{2/3}

B

l

C

m1/2m^{1/2}

D

m−1/2m^{- 1/2}

Answer

m−1/2m^{- 1/2}

Explanation

Solution

Gm×2ml2=m×2l34π2T2\frac{Gm \times 2m}{l^{2}} = m \times \frac{2l}{3}\frac{4\pi^{2}}{T^{2}}or T=(4π2l33Gm)1/2T = \left( \frac{4\pi^{2}l^{3}}{3Gm} \right)^{1/2}i.e. T∝m−1/2T \propto m^{- 1/2}