Question

The kinetic energy of a satellite in its orbit around the earth is $E$. What should be the minimum kinetic energy of the satellite so as to enable it to escape from the gravitational pull of the earth?

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

Answer 1

Answer: (B)

$2E$

We know that $v_e=\sqrt{2}{v}_0$. where $v_0$ is orbital velocity.
$K.E.$ in the orbit, $E=\frac{1}{2}M{v}_0^2$
$K.E.$ to escape $E=\frac{1}{2}M{v}_e^2=\frac{1}{2}M\left(2v_0^2\right)=\frac{1}{2}M{v}_0^2\times 2=2E$