A binary star consists of two stars A (mass ) and B (mass ), where is the mass of the sun. They are separated by distance and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the

Question

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 [2010]

Smart Achievers · Accepted Answer

(6)

Let the center of mass of the binary star system be at the origin 'O'. Distance between $A O = x$ and $O B = (d - x)$

$0 = \frac{2.2 M_{s} (- x) + 11 M_{s} (d - x)}{2.2 M_{s} + 11 M_{s}}$

$\Rightarrow 0 = 2.2 M_{s} (- x) + 11 M_{s} (d - x) \Rightarrow x = \frac{5 d}{6}$

For a binary star system, angular speed $ω$ about the centre of mass 'O' is same for both the stars.

$∴$ $\frac{L_{total}}{L_{B}} = \frac{2.2 M_{s} {(\frac{5 d}{6})}^{2} ω + 11 M_{s} {(\frac{d}{6})}^{2} ω}{11 M_{s} {(\frac{d}{6})}^{2} ω} = 6$

Solution

Want Us to Email you About Special Offers & Updates?