Question

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

Answer 1

answer : option (D)

explanation :Figure shows a planet in an elliptical orbit around the sun S. here external torque acts on planet equals zero. so, angular momentum of planet remains constant.

e.g., $mvr=\textbf{constant}$

where v is velocity of planet , m is mass of planet and r is radius of orbit.

so, it is clear that velocity is inversely proportional to radius of orbit.

means, velocity becomes maximum when radius of orbit becomes minimum.

in figure, we see radius of orbit is minimum at $P_4$

so, velocity of planet is maximum at $P_4$

and you know, kinetic is directly proportional to square of velocity that's why kinetic energy is maximum at $P_4$