JEE Mains · Physics · STD 11 - 7. gravitation
The angular momentum of a planet of mass \(M\) moving around the sun in an elliptical orbit is \(\overrightarrow{ L }\). The magnitude of the areal velocity of the planet is:
- A \(\frac{4 L }{ M }\)
- B \(\frac{L }{ M }\)
- C \(\frac{2L }{ M }\)
- D \(\frac{L }{2M }\)
Answer & Solution
Correct Answer
(D) \(\frac{L }{2M }\)
Step-by-step Solution
Detailed explanation
For small displacement ds of the planet its area can be written as \(d A =\frac{1}{2} rd \ell\) \(=\frac{1}{2} r d s \sin \theta\) A.vel \(=\frac{ d A }{ dt }=\frac{1}{2} r \sin \theta \frac{ ds }{ dt }=\frac{ Vr \sin \theta}{2}\)…
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