Question

If the potential energy of a satellite is $-2\text{MJ}$, then the binding energy of the satellite is

• A. $1\text{MJ}$
• B. $2\text{MJ}$
• C. $8\text{MJ}$
• D. $4\text{MJ}$

Answer 1

The correct option is A $1\text{MJ}$

Given:
$P.E.=-2\text{MJ}$

For a satellite of mass $m$ revolving around a planet of mass $M$ in a circular orbit of radius $r$.

So, the potential energy of satellite will be

$P.E.=-\frac{GMm}{r}$

And kinetic energy of satellite moving in an orbit will be

$\therefore K.E.=\frac{GMm}{2r}$

So, $T.E.=P.E.+K.E.$

$\Rightarrow T.E.=-\frac{GMm}{2r}$

Since, binding energy is the absolute value of total energy.

$\therefore$ Binding Energy $=|T.E|=\frac{GMm}{2r}$

So, binding energy $=\frac{|P.E|}{2}=1\text{MJ}$

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

Alternative method:

Binding energy $=-TE=-\frac{PE}{2}=1\text{MJ}$

$\begin{array}{c}\text{Why this question: To make students}\\ \text{understand the concept of a bound system}\\ \text{and its relationship with total energy.}\end{array}$