Earth revolves round the sun in a circular orbit of radius 'R'. The angular momentum of the revolving earth…

Earth revolves round the sun in a circular orbit of radius 'R'. The angular momentum of the revolving earth is directly proportional to
  1. $\mathrm{R}^{2}$
  2. $\mathrm{R}^{3}$
  3. $\sqrt{\mathrm{R}}$
  4. $\mathrm{R}$

Solution

Angular momentum of the earth, $\mathrm{L}=\mathrm{mVR} \quad \text { but } \quad \mathrm{V}=\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}}$ where $M$ is the mass of the sun $\begin{array}{l} \therefore L=m R \sqrt{\frac{G M}{R}}=m \sqrt{G M R} \\ \therefore L \propto \sqrt{R} \end{array}$

Asked in: MHT CET 2020 (13 Oct Shift 2)

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