Question

A binary star system consists of two stars. One star has twice the mass of the other. The star rotates about their common centre of mass. Which of the following statement is correct?

• A. Star having the smaller mass has twice angular momentum compared to heavier star
• B. Both stars have same angular momentum about centre of mass
• C. Both stars have same linear speed
• D. Both the stars have same kinetic energy

Answer 1

Answer: (A)

Let the distance between the two stars be $3 l$. Then, Angular momentum of mass $m$ about common centre of mass $=m(2 l)^{2} \omega$ Angular momentum of mass $2 m$ about common centre of mass $=(2 m) l^{2} \omega$
Their ratio is $\frac{(L)_{m}}{(L)_{2 m}}=\frac{m(2 l)^{2} \omega}{2 m l^{2} \omega}=2$