Two stars of masses M and 2M are at a distanc | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The two stars revolve around their common center of mass $(COM)$ with the same angular velocity $\omega$.Let $r_1$ and $r_2$ be the distances of m

Vedclass · Accepted Answer

$\sqrt{\frac{3 G M}{d^3}}$

Vedclass · Answer

(D) The two stars revolve around their common center of mass $(COM)$ with the same angular velocity $\omega$.Let $r_1$ and $r_2$ be the distances of masses $M$ and $2M$ from the $COM$,respectively.We know that $r_1 + r_2 = d$ and $M r_1 = (2M) r_2$.From these,$r_1 = \frac{2M}{3M} d = \frac{2}{3} d$.The gravitational force between the stars provides the necessary centripetal force for the star of mass $M$:$F_g = F_c$$\frac{G(M)(2M)}{d^2} = M \omega^2 r_1$Substituting $r_1 = \frac{2}{3} d$:$\frac{2 G M^2}{d^2} = M \omega^2 \left(\frac{2}{3} d\right)$$\frac{2 G M}{d^2} = \omega^2 \left(\frac{2}{3} d\right)$$\omega^2 = \frac{2 G M}{d^2} \cdot \frac{3}{2 d} = \frac{3 G M}{d^3}$$\omega = \sqrt{\frac{3 G M}{d^3}}$

Two stars of masses $M$ and $2M$ are at a distance $d$ apart and are revolving around their common center of mass. The angular velocity of the system of the two stars is ($G$ is the universal gravitational constant).

Similar Questions

$A$ planet of mass $m$ moves in an ellipse around the sun of mass $M_S$ such that its maximum and minimum distances are $r_1$ and $r_2$ respectively. The angular momentum of the planet relative to the center of the sun is

Write the equation for the orbital velocity of a satellite revolving very close to the surface of the Earth.

Imagine a light planet revolving around a very massive star in a circular orbit of radius $R$ with a period of revolution $T$. If the gravitational force of attraction between the planet and the star is proportional to $R^{-5/2}$,then ${T^2}$ is proportional to:

$A$ geostationary satellite is orbiting the earth at a height of $5R$ above the surface of the earth,where $R$ is the radius of the earth. The time period of another satellite in hours at a height of $2R$ from the surface of the earth is:

Two satellites $A$ and $B$ are orbiting in circular paths of radii $4R$ and $R$ respectively. If the orbital velocity of satellite $A$ is $3V$,what is the orbital velocity of satellite $B$ (in $V$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module