A system of binary stars of masses MA and MB are moving in circular orbits of radii RA and RB respectively. If TA and TB are the time periods of masses MA and MB respectively, then

Question

A system of binary stars of masses MA and MB are moving in circular orbits of radii RA and RB respectively. If TA and TB are the time periods of masses MA and MB respectively, then (A) (TA/TB)=((RA/RB))1 / 2 (B) TA >TB(. if . RA > RB) (C) TA >TB(. if . MA > MB) (D) TA=TB

Tardigrade Admin · Accepted Answer

In case of binary star system both the stars rotate with same angular velocity ω about their centre of mass in their respective orbits. ∴ ω=(2 π/TA)=(2 π/TB) or TA=TB

Q. 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

$\frac{T _{A}}{T _{B}} = (\frac{R _{A}}{R _{B}})^{1/2}$

$T_{A} > T_{B} ($ if $R_{A} > R_{B})$

$T_{A} > T_{B} ($ if $M_{A} > M_{B})$

$T_{A} = T_{B}$

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

Q. A system of binary stars of masses MA​ and MB​ are moving in circular orbits of radii RA​ and RB​ respectively. If TA​ and TB​ are the time periods of masses MA​ and MB​ respectively, then

TB​TA​​=(RB​RA​​)1/2

TA​>TB​( if RA​>RB​)

TA​>TB​( if MA​>MB​)

TA​=TB​