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7.Gravitation
medium
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
$\frac{L }{2M }$
(JEE MAIN-2021)
Solution
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 $=\frac{ d A }{ dt }=\frac{1}{2} r \sin \theta \frac{ ds }{ dt }=\frac{ Vr \sin \theta}{2}$
$\frac{ d A }{ dt }=\frac{1}{2} \frac{ mVr \sin \theta}{ m }=\frac{ L }{2 m }$
Standard 11
Physics
