Question

A double star consists of two stars having masses m and 2m separated by a distance r. Which of the following statement is correct?

• A. Radius of circular path of star of mass 2m is $\frac{2r}{3}$
• B. Kinetic energy of 2 m mass star is double that of lighter star
• C. Time period of revolutionof both are not same
• D. Angular momentum of lighter star about their centre of mass is more

Answer 1

The correct option is D

Angular momentum of lighter star about their centre of mass is more

$r_1=\frac{2r}{3}$ and $r_2=\frac{r}{3}$

$\omega$ will be same for both the stars.

$K_1=\frac{1}{2}{I}_1{\omega }^2$ and $K_2=\frac{1}{2}{I}_2{\omega }^2$

$\therefore$ =$\frac{K_1}{K_2}=\frac{I_1}{I_2}=\frac{m{\left(\frac{2r}{3}\right)}^2}{2m{\left(\frac{r}{3}\right)}^2}=2$

$L_1=I_1\omega$

and $L_2=I_2\omega$

$\therefore$ $\frac{L_1}{L_2}=\frac{I_1}{I_2}=2$