Question

An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the earth's surface. Total energy is always constant at any orbit. (Radius of the earth is $6400km$)
The height of the satellite above the Earth surface

• A. $6400km$
• B. $3200km$
• C. $9600km$
• D. $4800km$

Answer 1

The correct option is A $6400km$

$\begin{array}{c}{v}_0=\frac{v_e}{2}\\ \therefore \sqrt{\frac{GM}{r}}=\frac{\sqrt{\frac{2GM}{R}}}{2}\\ \therefore r=2R\\ or,h=r-R=R\\ or,height=radiusofearth\\ weknow,\\ radiusofearth=6400Km\end{array}$

Hence,

option $\left(A\right)$ is correct answer.