The orbital angular momentum of a satellite r | vedclass

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(D) The orbital angular momentum $L$ of a satellite of mass $m$ revolving at a distance $r$ from the center of a planet of mass $M$ is given by $L = m

Vedclass · Accepted Answer

$4 L$

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(D) The orbital angular momentum $L$ of a satellite of mass $m$ revolving at a distance $r$ from the center of a planet of mass $M$ is given by $L = mvr$.Since the orbital velocity $v = \sqrt{\frac{GM}{r}}$,we substitute this into the expression for $L$:$L = m \sqrt{\frac{GM}{r}} \cdot r = m \sqrt{GMr}$.From this expression,we can see that $L \propto \sqrt{r}$.Let $L_1 = L$ at distance $r_1 = r$,and $L_2$ be the new angular momentum at distance $r_2 = 16r$.Then,$\frac{L_2}{L_1} = \sqrt{\frac{r_2}{r_1}} = \sqrt{\frac{16r}{r}} = \sqrt{16} = 4$.Therefore,$L_2 = 4L_1 = 4L$.

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 momentum will be

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