A binary star system consists of two stars of masses M₁ and M₂ revolving in circular orbits of radii R₁ and R₂ respectively. If their respective time periods are T₁ and T₂, then

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$T_{1} > T_{2} i f R_{1} > R_{2}$

$T_{1} > T_{2} i f M_{1} > M_{2}$

$T_{1} = T_{2}$

$\frac{T_{1}}{T_{2}} = {(\frac{R_{1}}{R_{2}})}^{\frac{3}{2}}$

answer is C.

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Detailed Solution

In a binary star system, the two stars move under their mutual gravitational force. Therefore, their angular velocities and hence their time periods are equal. Thus the correct choice is (c).

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