Question

Angular momentum of earth revolving around the sun in a circular orbit of radius R is proportional to

• A. \(\sqrt{R}\)
• B. \(R\)
• C. \(R^2\)
• D. \(R^{1/3}\)
• E. \(R^{3/2}\)

Hint:

In orbital motion, velocity varies as \(1/\sqrt{R}\), so angular momentum varies as \(\sqrt{R}\).

Answer 1

The Correct Option is A

Concept: Angular momentum: \[ L = mvr \] For circular orbit: \[ \frac{mv^2}{R} = \frac{GMm}{R^2} \Rightarrow v = \sqrt{\frac{GM}{R}} \]

Step 1: Substitute velocity. \[ L = mR \cdot \sqrt{\frac{GM}{R}} = m\sqrt{GMR} \]

Step 2: Simplify relation. \[ L \propto \sqrt{R} \]

Step 3: Conclusion. \[ \boxed{\sqrt{R}} \]