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Q.

The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is L→ . The magnitude of the areal velocity of the planet is:

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a

LM

b

2LM

c

L2M

d

4LM

answer is C.

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Detailed Solution

Assuming SAB a triangle  A=12r2θ ⇒dAdt=12r2dθdt ⇒dAdt=12r2ω  Now, Angular Momentum, L=Iω=Mr2ω ⇒r2ω=LM Thus , dAdt=12LM ⇒Areal velocity=dAdt=L2M
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