Question

A satellite is revolving round the earth with orbital speed $v_0$. If it stops suddenly, the speed with which it will strike the surface of earth would be

($v_e$= escape velocity of a particle on earth's surface)

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Let r be the radius of the satellite.Then

$v_0^2=\frac{GM}{r}$ ------------------(1)

R = radius of earth.

Applying conservation of mechanical energy between points A and B, we have:

$\frac{1}{2}m{v}^2=-\frac{GMm}{r}-(-\frac{GMm}{R})$

or $v^2=2\frac{GM}{R}-\frac{2GM}{r}$

= $v_e^2-2v_0^2$

or $v=\sqrt{v_e^2-2v_0^2}$