Question

The orbital angular momentum of a satellite revolving at a distance $r$ from the centre is $L .$ If the distance is increased to $16 r$, then the new angular momentum will be

• A. $16\, L$
• B. $64\, L$
• C. $\frac{L}{4}$
• D. $4\, L$

Answer 1

Answer: (D)

$L=m v r=m \sqrt{\frac{G M}{r}} r=m \sqrt{G M r}$
$\therefore L \propto \sqrt{r}$
$\Rightarrow \frac{L_{2}}{L_{1}} =\sqrt{\frac{r_{2}}{r_{1}}}$
$=\sqrt{\frac{16 r}{r}}=4$
$\Rightarrow L_{2}=4\, L$