Question

For a planet-satellite system, which of the folowing statements is incorrect?

• A. $|T.E|=|K.E|$
• B.
  $|U|=2|K.E|$
• C. It is a bounded system.
  
• D. $|U|=|K.E|$
  

Answer 1

The correct option is D $|U|=|K.E|$


Let us consider a satelite of mass $m$ revolving around a planet of mass $M$ at an orbital radius $r$.

Kinetic energy of the satellite is given by,

$K.E=\frac{1}{2}m{v_o}^2$

$K.E=\frac{1}{2}m\frac{GM}{r}(\because v_o=\sqrt{\frac{GM}{r}})$

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

Potential energy of the system is given by,

$U=-\frac{GMm}{r}$

Now, Total energy of the system is given by,

$T.E=K.E+U=\frac{GMm}{2r}+(\frac{-GMm}{r})$

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

$\Rightarrow |T.E|=|K.E|$

$\Rightarrow |U|=2|K.E|$

Also, negative sign in the expression of $T.E$ shows that the system is a bounded one.

Hence, option $\left(D\right)$ is the correct answer.