A system of binary stars of masses M1 and M2 are moving in circular orbits of radii r1 and r2 respectively. If T1 and T2 are the time periods of revolution of masses M1 and M2 respectively and if (r1/r2)=2, then find (T1/T2).

Question

A system of binary stars of masses M1 and M2 are moving in circular orbits of radii r1 and r2 respectively. If T1 and T2 are the time periods of revolution of masses M1 and M2 respectively and if (r1/r2)=2, then find (T1/T2). (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Centre fo mass of binary star lies at certre of their circular path.

M_{1} r_{1} = M_{2} r_{2}

Then,

G \frac{M _{1} M _{2}}{( r _{1} + r _{2} ) ^{2}} = M_{1} ω_{1}^{2} r_{1} = M_{2} ω_{2}^{2} r_{2}

\Rightarrow ω_{1} = ω_{2} \to \frac{T _{1}}{T _{2}} = 1.00

Same angular velocity and time period of revolution.

Q. A system of binary stars of masses M1​ and M2​ are moving in circular orbits of radii r1​ and r2​ respectively. If T1​ and T2​ are the time periods of revolution of masses M1​ and M2​ respectively and if r2​r1​​=2, then find T2​T1​​.

Centre fo mass of binary star lies at certre of their circular path. M1​r1​=M2​r2​ Then, G(r1​+r2​)2M1​M2​​=M1​ω12​r1​=M2​ω22​r2​ ⇒ω1​=ω2​→T2​T1​​=1.00 Same angular velocity and time period of revolution.