# 58 : Figure shows a planet in an elliptical orbit around the sun S. Where is the kinetic energy of the planet maximum (A) P1          (B) P3             (C) P3         (D)  P4

Dear Student,

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 $\propto$ v2                                     --- ( 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 ' p3 ' ( As p3 is closest to the Sun ( S ) )  ,  So from equation 1 we can say that

Kinetic energy also maximum at at the point ' p3 '

So,

Option ( C )                                                                            ( Ans )