Q. A binary star consists of two stars $A$ (mass 2.2 $M_{s}$) and B (mass 11 $M_{s}$), where $M_{s}$ is the mass of the sun. They are separated by distance $d$ and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star $B$ about the centre of mass is
A) 7
B) 6
C) 9
D) 10
Explanation
(b) $\frac{L_{Total}}{L_{B}} = \frac{(I_{A} + I_{B})\omega}{I_{B}.\omega}$ (as $\omega$ will be same in both cases)
$= \frac{I_{A}}{I_{B}} + 1 = \frac{m_{A}r_{A}^{2}}{m_{B}r_{B}^{2}} + 1$
$= \frac{r_{A}}{r_{B}} + 1$ (as $m_{A}r_{A} = m_{B}r_{B})$
$= \frac{11}{2.2} + 1$ $(as\ \ r \propto \frac{1}{m})$
$= 6$
$\therefore$ The correct answer is 6.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.