Question

A binary star system consists of two stars of masses $M_1\,and\,M_2$ revolving in circular orbits of radii $R_1\,and\,R_2$ respectively. If the respective time periods are $T_1\,and\,T_2$

• A. $T_1>T_2\,if\,R_1>R_2$
• B. $T_1>T_2\,if\,M_1>M_2$
• C. $T_1=T_2$
• D. $\frac{T_1}{T_2}=\left(\frac{R_1}{R_2}\right)^{3/2}$

Answer 1

Answer: (C)

In a binary star system, there are two stars moving under their mutual gravitational force of attraction. Their angular velocities are equal and hence their periodic times are also equal.
$\left[\because \omega=\frac{2 \pi}{T}\right]$
$\therefore T_{1}=T_{2}$