Question

Earth revolves round the sun in a circular orbit of radius $R$. The angular momentum of the revolving earth is directly proportional to

• A. $R^2$
• B. $R^3$
• C. $\sqrt{R}$
• D. $R$

Hint:

For planets in circular orbit, angular momentum depends on orbital radius through velocity.

Answer 1

The Correct Option is C

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 $\sqrt{R}$.