CameraIcon

SearchIcon

MyQuestionIcon

1

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

Kepler's Law

Two satellite...

Question

Two satellites A and B of masses $m_{1}$ and $m_{2} (m_{1} = 2 m_{2})$ are moving in circular orbits of radii $r_{1}$ and $r_{2} (r_{1} = 4 r_{2})$ , respectively, around the earth. If their periods are $T_{A}$ and $T_{B}$ , then the ratio $T_{A} / T_{B}$ is

A

4

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

B

16

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

C

2

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

D

8

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

Open in App

Solution

The correct option is B 8
Kepler second law - square of time period is proportional to cube of radius of orbit.
$∴ T^{2} α r^{3}$
In this case, $r_{1} = 4 r_{2} \Rightarrow \frac{r_{1}}{r_{2}} = 4$
$T_{A}^{2} α r_{1}^{3}$ and $T_{B}^{2} α r_{2}^{3}$
$∴ \frac{T_{A}}{T_{B}} = (\frac{r_{1}}{r_{2}})^{\frac{3}{2}} = (4^{\frac{1}{2}})^{3}$
$\Rightarrow \frac{T_{A}}{T_{B}} = 8$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Two satellite of masses

m_{1}

m_{2} (m_{1} > m_{2})

are revolving around earth in circular orbits of radii

r_{1}

r_{2} (r_{1} > r_{2})

respectively. Which of the following statements is true regarding their velocities

V_{1}

V_{2}

.

Q. Two satellites,

A

B

m

2 m

A

is in a circular orbit of radius

R

B

in a circular orbit of radius

2 R

around the earth. The ratio of their kinetic energies,

\frac{T_{A}}{T_{B}}

Q. Two satellites,

A

B

m

2 m

A

is in circular orbit of radius

R

B

is in a circular orbit of radius

2 R

around the earth. The ratio of their kinetic energies,

T_{A} / T_{B}

Q. A system of binary stars of masses

m_{A}

m_{B}

are moving in circular orbits of radii

r_{A}

r_{B}

respectively. If

T_{A}

T_{B}

are the time periods of masses

m_{A}

m_{B}

respectively, then

Q. Two satellites of mass

m_{1}

m_{2} (m_{1} > m_{2})

revolve round the earth in circular orbits of radii

r_{1}

r_{2}

(r_{1} > r_{2})

Their speeds are related as

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Kepler's Law

PHYSICS

Watch in App

explore_more_icon

Explore more

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon