Target Exam

CUET

Subject

Physics

Chapter

Gravitation

Question:

A satellite orbits around the earth in a circular orbit with a speed v and orbital radius r. If it loses some energy, then v and r changes as

Options:

v decreases and r increases

both v and r decrease

v increases and r decreases

both v and r increase

Correct Answer:

v increases and r decreases

Explanation:

Total energy of a satellite orbiting in radius r is

E = KE + Pot E = $\frac{1}{2} m v^2-\frac{G M m}{r}$

Where $\frac{GMm}{r^2}=\frac{mv^2}{r}$

$v=\sqrt{\frac{GM}{r}}$

$=\frac{1}{2} m \frac{GM}{r}-\frac{GMm}{r}=-\frac{GMm}{2 r}$

If it loses some energy r must decrease

∴  v = $\sqrt{\frac{GM}{r}}$, v increases