Question

When a satellite is going round the earth in a circular orbit of radius $r$ and speed $v$ loses some of its energy, then $r$ and $v$ change as:

• A. $r$ and $v$ both will increase
• B. $r$ and $v$ both will decrease
• C. $r$ will decrease and $v$ will increase
• D. $r$ will increase and $v$ will decrease

Answer 1

Answer: (C)

$r$ will decrease and $v$ will increase

kinetic energy of the satellite rotating at in a orbit of radius r is, $=\frac{1}{2}\frac{mGM}{r}$

and potential energy is given by, $=-\frac{mMG}{r}$

total energy $=-\frac{1}{2}\frac{mGM}{r}$

so we can say that $P=2T,K=-T$

if energy of the body decreases then magnitude has to increase because total energy is with negative sign.

so for as energy decrease and magnitude increases then $r$ decreases.

and as r decreases then $K$ increases, so increases its velocity.

so best possible answer is C.