Physics - Gravitation Question with Solution | TestHub

The orbital velocity of the earth revolving around the sun is given by $v=\sqrt{\frac{GM}{R}}$.

The angular momentum of the earth is $L=mvR$.

Substituting the value of $v$, we get $L=m\sqrt{\frac{GM}{R}}R=m\sqrt{GM}{R}^{1/2}$.

Since $m$, $G$, and $M$ are constants, $L\propto R^{1/2}$.

Comparing this with $L\propto R^n$, we get $n=0.5$.

Answer: 0.5