Question

The K.E. of a satellite in an orbit close to the surface of the earth is $E$. Its maximum K.E. to not escape from the gravitational field of the earth is

• A. $2E$
• B. $4E$
• C. $2\sqrt{2}E$
• D. $\sqrt{2}E$

Answer 1

The correct option is A $2E$

Orbital velocity near the surface of the earth is given by

$v=\sqrt{\frac{GM}{R}}$

And kinetic energy will be

$E=\frac{1}{2}m{v}^2=\frac{GMm}{2R}$

Escape Velocity is given by

$v_e=\sqrt{\frac{2GM}{R}}$

So, maximum kinetic energy for escape velocity will be

$E^{\prime }=\frac{1}{2}m{v}_e^2=\frac{GMm}{R}$

Thus, $E^{\prime }=2E$

Hence, option $\left(a\right)$ is correct.