MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Newton's Law of Gravitation

A system of b...

Question

A system of binary stars of masses $m_{A}$ and $m_{B}$ are moving in circular orbits of radii $r_{A}$ and $r_{B}$ respectively. If $T_{A}$ and $T_{B}$ are the time periods of masses $m_{A}$ and $m_{B}$ respectively, then

A

\frac{T_{A}}{T_{B}} = (\frac{r_{A}}{r_{B}})^{3 / 2}

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

B

T_{A} > T_{B} (i f r_{A} > r_{B})

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

C

T_{A} > T_{B} (i f m_{A} > m_{B})

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

D

T_{A} = T_{B} [+ 3, - 1]

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

Open in App

Solution

The correct option is D $T_{A} = T_{B} [+ 3, - 1]$
Since both the stars move in circular orbit under influence of each other's forces, Applying $F = m a$ to both the stars and using $ω = \frac{2 π}{T}$ , we get

$\frac{G m_{A} m_{B}}{{(r_{A} + r_{B})}^{2}} = \frac{m_{A} r_{A} 4 π^{2}}{T_{A}^{2}} = \frac{m_{B} r_{B} 4 π^{2}}{T_{B}^{2}}$

Thus, $m_{A} r_{A} = m_{B} r_{B}$

Hence, $T_{A} = T_{B}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. A double star system consists of two stars

A

B

which have time periods

T_{A}

T_{B},

R_{A}

R_{B}

M_{A}

M_{B}

respectively. Then

Q. A double star system consists of two stars A and B which have time periods

T_{A}

T_{B}

R_{A}

R_{B}

M_{A}

M_{B}

. Choose the correct option.

Q. Two satellites A and B of masses

m_{1}

m_{2} (m_{1} = 2 m_{2})

are moving in circular orbits of radii

r_{1}

r_{2} (r_{1} = 4 r_{2})

, respectively, around the earth. If their periods are

T_{A}

T_{B}

, then the ratio

T_{A} / T_{B}

Q. When two bodies A and B are brought in contact with each other, heat flows from A to B, then .
(A and B have temperature

T_{A} a n d T_{B}

Q. The given figure shows the isotherms of a fixed mass of an ideal gas at three temperatures

T_{A}, T_{B}

T_{C}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Kepler's Law

PHYSICS

Watch in App

explore_more_icon

Explore more

Newton's Law of Gravitation

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon