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  • Consider a binary star system of star A and star B with masses and <img alt="\mathrm{m}_{\mathrm{B}}" src="/latex-image/?%5Cmathrm%7Bm%7D_%7B%5Cmathrm%7BB%7D

Consider a binary star system of star A and star B with masses \mathrm{m}_{\mathrm{A}} and \mathrm{m}_{\mathrm{B}} revolving in a circular orbit of radii \mathrm{r}_{\mathrm{A}} and \mathrm{r}_{\mathrm{B}}, respectively. If \mathrm{T}_{\mathrm{A}} and \mathrm{T}_{\mathrm{B}} are the time period of star A and star B, respectively,
then:
 
Option: 1 \frac{T_{\mathrm{A}}}{\mathrm{T}_{\mathrm{B}}}=\left(\frac{\mathrm{r}_{\mathrm{A}}}{\mathrm{r}_{\mathrm{B}}}\right)^{\frac{3}{2}}
Option: 2 \mathrm{T}_{\mathrm{A}}=\mathrm{T}_{\mathrm{B}}
Option: 3 \mathrm{T}_{\mathrm{A}}>\mathrm{T}_{\mathrm{B}}\left(\right.if \mathrm{m}_{\mathrm{A}}>\mathrm{m}_{\mathrm{B}} )
Option: 4 \mathrm{T}_{\mathrm{A}}>\mathrm{T}_{\mathrm{B}} (if \mathrm{r}_{\mathrm{A}}>\mathrm{r}_{\mathrm{B}} )

Answers (1)

best_answer

 

r_{A} \rightarrowthe radius of circular motion for mass m_{A}
r_{B} \rightarrowthe radius of circular motion for mass m_{B}.

\quad T_{A}=2 \pi\frac{ r_{A}}{V_{A}} \quad T_{B}=2 \pi \frac{r_{B}}{V_{B}}
In a Binary star system, their respective angular velocity is constant i.e

i.e \: \omega_{A}=\omega _{B}

\frac{V_{A}}{r_{A}}=\frac{V_{B}}{r B} \Rightarrow T_{A}=T_{B}
The correct option is (2)

Posted by

vishal kumar

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