Question

Assuming that the earth is revolving around the sun in circular orbit of radius R, the angular momentum is directly proportional to $R^n$. The value of 'n' is

• A. 2
• B. 1.5
• C. 1
• D. 0.5

Answer 1

Answer: (D)

0.5

Answer 2

Using the formula for angular momentum

$L = mvr$,

and equating centripetal force to gravitational force, we have

$\frac{mv^2}{R} = \frac{GMm}{R^2} \quad \Rightarrow \quad v = \sqrt{\frac{GM}{R}}$.

Thus,

$L = mR\sqrt{\frac{GM}{R}} = m\sqrt{GMR} \quad \Rightarrow \quad L \propto \sqrt{R} = R^{\frac{1}{2}}$.