Gravitation Question 297

Question: In planetary motion the areal velocity of position vector of a planet depends on angular velocity$ [(\omega )] $ and the distance of the planet from sun (r). If so, the correct relation for areal velocity is

Options:

A) $ [\frac{dA}{dt}\propto \omega r] $

B) $ [\frac{dA}{dt}\propto {{\omega }^{2}}r] $

C) $ [\frac{dA}{dt}\propto \omega r^{2}] $

D) $ [\frac{dA}{dt}\propto \sqrt{\omega r}] $

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Answer:

Correct Answer: C

Solution:

  • $ [\frac{dA}{dt}=\frac{L}{2m}\Rightarrow \frac{dA}{dt}\propto vr\propto \omega r^{2}] $


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