A planet is revolving around the sun in an elliptical orbit. Its closest distance from the sun is r_min The farthest distance from the sun is r_max If the orbital angular velocity of the planet when it is nearest to the sun is $ω$ then the orbital angular velocity at the point when it is at the farthest distance from the sun is

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$\sqrt{(r_{max} / r_{min})} ω$

$(r_{max}^{2} / r_{min}^{2}) ω$

$\sqrt{(r_{min} / r_{max})} ω$

$({r_{min}}^{2} / {r_{max}}^{2}) ω$

answer is D.

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Detailed Solution

$\begin{array}{l} v_{1} r_{1} = v_{2} r_{2} or r_{1}^{2} ω_{1} = r_{2} ω_{2} \\ or r_{min}^{2} ω = r_{max}^{2} ω^{'} \\ ω^{'} = (r_{min}^{2} / r_{max}^{2}) ω \end{array}$

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