Question

The distance between the sun and the earth be $r$, then the angular momentum of the earth around the sun is proportional to

• A. $\sqrt{r}$
• B. $r^{3/2}$
• C. $r$
• D. None of these

Answer 1

Answer: (A)

$\sqrt{r}$

Answer 2

By Kepler's third law of planetary motion,
we have, $T^{2} \propto a^{3}$
$\Rightarrow T \propto a^{3 / 2}$
Given a $=r$ and $\omega=\frac{2 \pi}{T}$
= angular speed $=\omega \propto r^{-3 / 2}$
Also angular momentum $L=m r^{2} \omega$
$\Rightarrow L \propto r^{2} \times r^{-3 / 2}$
$\Rightarrow L \propto r^{3 / 2}$