The earth moves around the sun in an elliptical orbit as shown in figure. The ratio $\frac{O A}{O B} = x$ . The ratio of the speed of the earth at B to that at A is nearly

\sqrt{x}

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x

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x \sqrt{x}

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x^{2}

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Solution

The correct option is B $x$
Using the conservation of angular momentum, mvr=const
$\Rightarrow m v_{A} r_{A} = m v_{B} r_{B} ∴ \frac{v_{B}}{v_{A}} = \frac{r_{A}}{r_{B}} = x$

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