A satellite is revolving in a circular orbit at a height 'h' above the surface of the earth of radius 'R'. The speed of the satellite in its orbit is one-fourth the escape velocity from the surface of the earth. The relation between 'h' and 'R' is

h = 2 R

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

h = 3 R

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

h = 5 R

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

h = 7 R

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

Open in App

Solution

The correct option is D $h = 7 R$
We know that escape velocity, $v_{e} = \sqrt{\frac{2 G M}{R}}$ where $M$ =mass of earth

Now, speed $v = \frac{v_{e}}{4} = \frac{1}{4} \sqrt{\frac{2 G M}{R}}$

Now, centripetal force for orbitting = gravitational force

$⟹ \frac{m v^{2}}{(R + h)} = \frac{G M m}{(R + h)^{2}}$

$⟹ v^{2} = \frac{G M}{R + h}$

$⟹ \frac{1}{16} \frac{2 G M}{R} = \frac{G M}{R + h}$

$⟹ \frac{1}{8 R} = \frac{1}{R + h}$

$⟹ R + h = 8 R$

$⟹ h = 7 R$

Hence, answer is option-(D).

Suggest Corrections

Similar questions

Q. A satellite is revolving in a circular orbit at a height

^{'} h^{'}

from the earth's surface (radius of earth

R

;

h < < R

). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to:(Neglect the effect of atmosphere.)

Q. A satellite is revolving in a circular orbit at a height 'h' from the earth's surface(radius of earth R

;

<<

R). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is closed to(Neglect the effect of atmosphere.)

Q. A satellite is revolving in a circular orbit at a height '

h

' from the earth's surface (radius of earth

R

;

h << R

). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to (Neglect the effect of atmosphere.)

A satellite is revolving in a circular orbit at a height ‘h’ from the earth’s surface (radius of earth R ; $h << R$ ). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth’s gravitational field, is close to : (Neglect the effect of atmosphere.)

Q. A satellite is revolving in a circular orbit at a height h from the earth surface, such that h << R where R is the radius of the earth. Assuming that the effect of earth's atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is :

Join BYJU'S Learning Program

A satellite is revolving in a circular orbit at a height 'h' above the surface of the earth of radius 'R'. The speed of the satellite in its orbit is one-fourth the escape velocity from the surface of the earth. The relation between 'h' and 'R' is

The correct option is D h=7RWe know that escape velocity, ve=√2GMR where M=mass of earthNow, speed v=ve4=14√2GMRNow, centripetal force for orbitting = gravitational force⟹mv2(R+h)=GMm(R+h)2⟹v2=GMR+h⟹1162GMR=GMR+h⟹18R=1R+h⟹R+h=8R⟹h=7RHence, answer is option-(D).