Question

A satellite is revolving around the earth with a kinetic energy$E$. The minimum addition of kinetic energy needed to make its escape from its orbit is

• A. $2E$
• B. $\surd E$
• C. $E/2$
• D. $\surd E/2$
• E. $E$

Answer 1

The correct option is A

$2E$

Step 1. Given data

Kinetic energy of satellite =$E$.

Escape energy = $E_K$

Gravitational constant = $G$

Mass of the earth = $M$

Mass of satellite = $m$

Radius of the earth = $R$

Step 2. Find the Kinetic energy for escaping:

Kinetic energy of the satellite is,

$E=\frac{GMm}{2R}$

Energy required to escape from gravitational field is,

$E_K=\frac{GMm}{R}$

In the above equation, divide and multiply by$2$,

$E_K=2\left(\frac{GMm}{2R}\right)$

$=2E$

Hence, (A) option is correct .