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

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

KEAMKEAM 2011System of Particles and Rotational Motion

Solution:

For an orbit, angular momentum is conserved and this leads to one of Kepler's laws. For a circular orbit angular momentum is
$L=mvr =m \sqrt{\frac{GM}{r}}r$
Hence $L \propto \sqrt{r}$