Question

A system of binary stars of masses $M_{A}$ and $M_{B}$ are moving in circular orbits of radii $R_{A}$ and $R_{B}$ respectively. If $T_{A}$ and $T_{B}$ are the time periods of masses $M_{A}$ and $M_{B}$ respectively, then

• A. $\frac{T_{A}}{T_{B}}=\left(\frac{R_{A}}{R_{B}}\right)^{1 / 2}$
• B. $T_{A} >T_{B}\left(\right.$ if $\left. R_{A} > R_{B}\right)$
• C. $T_{A} >T_{B}\left(\right.$ if $\left. M_{A} > M_{B}\right)$
• D. $T_{A}=T_{B}$

Answer 1

Answer: (D)

In case of binary star system both the stars rotate with same angular velocity $\omega$ about their centre of mass in their respective orbits.
$\therefore \omega=\frac{2 \pi}{T_{A}}=\frac{2 \pi}{T_{B}}$
or $T_{A}=T_{B}$