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

Why can the entire surface of the Earth be viewed with the help of a polar satellite?

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 $V$)?

The radii of circular orbits of two satellites $A$ and $B$ of the earth are $4R$ and $R$ respectively,where $R$ is the radius of the earth. If the speed of satellite $B$ is $6V$,then the speed of satellite $A$ will be:

$A$ planet revolves around the Sun in an elliptical orbit. When it is closest to the Sun,its distance from the Sun is $d_1$ and its velocity is $v_1$. When it is farthest from the Sun,its distance from the Sun is $d_2$. What is its velocity at that point?

What is the ratio of the time periods of a satellite $A$ of mass $m$ at a distance $r$ from the center of the Earth and a satellite $B$ of mass $2m$ at a distance $2r$ from the center of the Earth?

Vedclass Test Series

Exam Paper Generator

Online Exam Module