Question

If the distance between sun and earth is \(d\), then the angular momentum of earth around the sun is proportional to

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

Hint:

For orbital motion: \[ v=\sqrt{\frac{GM}{r}} \] Then substitute into \[ L=mvr \] to get the dependence on \(r\).

Answer 1

The Correct Option is C

Angular momentum: \[ L = mvr \] For circular orbit: \[ v=\sqrt{\frac{GM}{r}} \] So, \[ L = mr\sqrt{\frac{GM}{r}} = m\sqrt{GMr} \] Thus, \[ L\propto \sqrt{r} \] If \(r=d\), then: \[ L\propto d^{1/2} \] So the direct calculation gives: \[ \boxed{\sqrt{d}} \] which corresponds to option (A), not (C).