Question

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

Easy

Solution

$L = m v r = m \sqrt{\frac{G M}{r}} r = m \sqrt{G M r}$
$∴ L \propto \sqrt{r}$ $\Rightarrow \frac{L_{1}}{L_{2}} = \sqrt{\frac{r_{1}}{r_{2}}} (\begin{matrix} ∵ L_{1} = L \\ r_{1} = r \\ r_{2} = 16 r \end{matrix})$
$\Rightarrow \frac{L}{L_{2}} = \sqrt{\frac{r}{16 r}} \Rightarrow \frac{L}{L_{2}} = \frac{1}{4} \Rightarrow L_{2} = 4 L$

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