If r denotes distance between sun and earth, then angular momentum of earth around sun is proportion

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7.Gravitation

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

A

$r^3/r$

B

$r$

C

$\sqrt r$

D

$r^2$

Solution

For an orbit, angular momentum is conserved and this leads to one of Kepler's laws. For a circular orbit angular momentum is

$\mathrm{L}=\mathrm{mvr}=\mathrm{m} \sqrt{\frac{\mathrm{GM}}{\mathrm{r}}} \mathrm{r}$

Hence

$\mathrm{L} \propto \sqrt{\mathrm{r}}$

Standard 11

Physics

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