The Earth moves around the Sun in an elliptical orbit as shown in figure. If the ratio OAOB=x, then the ratio of the speed of the Earth at B to that at A is nearly:

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The Earth moves around the Sun in an elliptical orbit as shown in figure. If the ratio $\frac{O A}{O B} = x$ , then the ratio of the speed of the Earth at $B$ to that at $A$ is nearly:

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$x$

$x \sqrt{x}$

$x^{2}$

$\sqrt{x}$

answer is B.

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Detailed Solution

Applying conservation of angular momentum at position $A and B$ ${mv}_{A} \times OA = {mv}_{B} \times OB; Hence, \frac{v_{B}}{v_{A}} = \frac{OA}{OB} = x$