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Question

# A planet revolving in an elliptical orbit has : A). a constant velocity of revolution. B). the least velocity when it is nearest to the sun. C). its areal velocity directly proportional to its velocity. D). its areal velocity inversely proportional to its velocity. E). a trajectory such that the areal velocity is constant. Choose the correct statement from the options given below :

A
A only
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B
E only
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C
D only
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D
C only
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Solution

## The correct option is B E only From law of conservation of angular momentum, Iω= constant ⇒mr2×vr= constant So, mvr= constant ⇒ Linear velocity of planet changes as radial distance from the sun changes. ⇒ Linear velocity is inversely proportional to the radial distance from the sun. Therefore, velocity is more when near to the sun. ⇒ Areal velocity, dAdt=L2m= constant ​​​​​​ Hence, option (B) is correct.

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