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

According to Kepler's third law $T^{2} \propto r^{3}$ $\Rightarrow T \propto r^{3 / 2}$ We have $\omega=\frac{2 \pi}{T}$ $\therefore \omega \propto r^{-3 / 2}$ Now, $L=m r^{2} \omega$ $\Rightarrow L \propto r^{2} \times r^{-3 / 2}$ $\therefore L \alpha r^{1 / 2}$