The minimum and maximum distances of a satellite revolving around earth are $2 R$ and $6 R$ respectively. Where $R$ is radius of earth. The maximum velocity of satellite is :-

\sqrt{\frac{G M}{R}}

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

\sqrt{\frac{3 G M}{2 R}}

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

\frac{1}{2} \sqrt{\frac{3 G M}{R}}

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

\sqrt{\frac{3 G M}{R}}

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

Open in App

Solution

The correct option is C $\frac{1}{2} \sqrt{\frac{3 G M}{R}}$
Let the $v_{1}$ and $v_{2}$ are the velocity of satellite in $2 R$ and $6 R$ path.

By the conservation of angular momentum
$m v_{1} 2 (R) = m v_{2} (6 R)$

$\Rightarrow v_{2} = \frac{v_{1}}{3} \dots (i)$

By the conservation of energy

$\frac{1}{2} m v_{1}^{2} - \frac{G M m}{2 R} = \frac{1}{2} m v_{2}^{2} - \frac{G M m}{6 R} . . . (i i)$

From equation (i) and (ii)

$v_{1} = \frac{1}{2} \sqrt{\frac{3 G M}{R}}$

Hence, $(D)$ is the correct answer.

Suggest Corrections

Similar questions

Q. Minimum and maximum distance of a satellite from the center of earth are

2 R

and

4 R

respectively where

R

is radius of earth. Radius of curvature at the point when satellite is at a distance

2 R

n R

, here

n

is(Answer upto two decimal places)

Q. The minimum and maximum distances of a satellite from the centre of the Earth are 2R and 4R respectively, where R is the radius of Earth and M is the Earth.Find radius of curvature at the point of the minimum distance.

The minimum and maximum distances of a satellite from the center of the Earth are 2R and 4R respectively, where R is the radius of Earth and M is the mass of Earth. The radius of curvature at the point of minimum distance is

Q. A geostationary satellite is orbiting the earth at a height

6 R

above the surface of the earth, where

R

is the radius of earth. The time period of another satellite revolving around earth at a height

2.5 R

from earth's surface is :

Q. A satellite is revolving around the earth in a circular orbit of radius a with velocity

v_{0}

. A particle is projected from it in backward direction with relative velocity

v = (\sqrt{\frac{7}{6}} + 1) v_{0}

. If maximum and minimum distances achieved by the particle from centre of earth are

r_{m a x}

and

r_{m i n}

respectively, then

Join BYJU'S Learning Program

The minimum and maximum distances of a satellite revolving around earth are 2R and 6R respectively. Where R is radius of earth. The maximum velocity of satellite is :-

The minimum and maximum distances of a satellite revolving around earth are $2 R$ and $6 R$ respectively. Where $R$ is radius of earth. The maximum velocity of satellite is :-