Binary stars of comparable masses rotate under the influence of each others gravity at a distance - 8G- 2-1-3- where - is the angular velocity of each of the system- If difference between the masses of two star is 6 units- Find the ratio of the masses of smaller to bigger star-

The correct option is B 1:7 REF.Image. m_2 m_1 = 6u r = ( 8Gω^2 )^1/3 a_1 = (F_net)m_1 = Gm_1m_2r^2 m_1 = Gm_2r^2 as; ω^2 r_1 = Gm_2r ...

You visited us 6 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Center of Mass as an Average Point

Binary stars ...

Question

Binary stars of comparable masses rotate under the influence of each others gravity at a distance ${[\frac{8 G}{ω^{2}}]}^{1 / 3}$ , where $ω$ is the angular velocity of each of the system. If difference between the masses of two star is 6 units. Find the ratio of the masses of smaller to bigger star.

4 : 10

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1 : 7

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

2 : 8

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 : 9

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $1 : 7$
REF.Image.
$m_{2} - m_{1} = 6 u$

$r = {(\frac{8 G}{ω^{2}})}^{1 / 3}$

$a_{1} = \frac{(F_{n e t})}{m_{1}} = \frac{G m_{1} m_{2}}{r^{2} m_{1}} = \frac{G m_{2}}{r^{2}}$

as; $ω^{2} r_{1} = \frac{G m_{2}}{r^{2}} . . . (1)$

and similarly
$ω^{2} r_{2} = \frac{G m_{1}}{r^{2}} . . . (i i)$

dividing (1) and (ii)
$\frac{r_{1}}{r_{2}} = \frac{m_{2}}{m_{1}}$
adding (i) and (ii)

$ω^{2} (r_{1} + r_{2}) = \frac{G}{r^{2}} (m_{1} + m_{2})$

$\Rightarrow ω^{2} r^{3} = G (m_{1} + m_{2}) = 8 G$

$\Rightarrow 8 G = G (m_{1} + m_{2})$ (On putting the value of $r$ from question)

$m_{1} + m_{2} = 8$

$m_{2} - m_{1} = 6 u$

$m_{1} + m_{2} = 8 u$

$m_{1} = 1 u$

$m_{2} = 7 u$

$m_{1} : m_{2} = 1 : 7$ Ans
Option (B)

Suggest Corrections

Similar questions

Q. In a binary star system, two stars of masses m and 2m distance r apart are revolving about their common centre of mass under their mutual gravitational attraction.
The ratio of angular momenta of two star about centre of mass is

Q. Two small dense stars rotate about their common centre of mass as a binary system with the period 1 year for each. One star is of double the mass of the other and the mass of the lighter one is 1/3 of the mass of the sun. The distance between the stars is xR if distance between the earth & the sun is R, find x.

In a binary star system, two stars of masses m and 2m distance r apart are revolving about their common centre of mass under their mutual gravitational attraction.

The ratio of kinetic energy of two stars is

Q. 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

Join BYJU'S Learning Program

Binary stars of comparable masses rotate under the influence of each others gravity at a distance [8Gω2]1/3, where ω is the angular velocity of each of the system. If difference between the masses of two star is 6 units. Find the ratio of the masses of smaller to bigger star.