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Question

The kinetic energies of a planet in an elliptical orbit about the sun at positions $A$ , $B$ and $C$ are $K_{A}$ , $K_{B}$ and $K_{C}$ respectively. $A C$ is the major axis and $S B$ is perpendicular to $A C$ at the position of the sun $S$ as shown in the figure with $S A < S B$ . Then,

A

K_{A} < K_{B} < K_{C}

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B

K_{A} > K_{B} > K_{C}

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C

K_{B} < K_{A} < K_{C}

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D

K_{B} > K_{A} > K_{C}

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Solution

The correct option is B $K_{A} > K_{B} > K_{C}$
$L = m v r = I ω = c o n s tan t K i n e t i c e n e r g y K = \frac{L^{2}}{2 I} I_{A} < I_{B} < I_{C} \Rightarrow K_{A} > K_{B} > K_{C}$

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