Question:
Earth revolves round the sun in a circular orbit of radius $R$. The angular momentum of the revolving earth is directly proportional to
Earth revolves round the sun in a circular orbit of radius $R$. The angular momentum of the revolving earth is directly proportional to
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For planets in circular orbit, angular momentum depends on orbital radius through velocity.
Updated On: Jan 30, 2026
- $R^2$
- $R^3$
- $\sqrt{R}$
- $R$
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The Correct Option is C
Solution and Explanation
Step 1: Expression for angular momentum.
\[ L = mvr \]
Step 2: Orbital speed of earth.
For circular orbit:
\[ v=\sqrt{\frac{GM}{R}} \]
Step 3: Substituting in angular momentum.
\[ L = mR\sqrt{\frac{GM}{R}} = m\sqrt{GM}\sqrt{R} \]
Step 4: Conclusion.
Angular momentum is proportional to $\sqrt{R}$.
\[ L = mvr \]
Step 2: Orbital speed of earth.
For circular orbit:
\[ v=\sqrt{\frac{GM}{R}} \]
Step 3: Substituting in angular momentum.
\[ L = mR\sqrt{\frac{GM}{R}} = m\sqrt{GM}\sqrt{R} \]
Step 4: Conclusion.
Angular momentum is proportional to $\sqrt{R}$.
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