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58 : Figure shows a planet in an elliptical orbit around the sun S. Where is the kinetic energy of the planet maximum

(A) P_{1} (B) P_{3} (C) P_{3} (D) P_{4}

Please find below the solution to the asked query:

We know formula for kinetic energy = k = $\frac{1}{2}{\mathrm{mv}}^{2}$ , Here the mass (m) of the object and the speed (v) of the object .

So,

k $\propto $ v

^{2}--- ( 1 )

And For given query , Angular momentum of the planet about Sun ( S ) is conserved , So

m v r = Constant , Then

v is maximum when ' r ' is minimum , So

' v ' is maximum at the point ' p

_{3}' ( As p

_{3}is closest to the Sun ( S ) ) , So from equation 1 we can say that

Kinetic energy also maximum at at the point ' p

_{3}'

So,

**Option ( C ) ( Ans )**

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