If the ratio of the distances of a planet from the sun at perihelion and aphelion is 2 : 3, then the ratio of their respective velocities at the perihelion and aphelion is
KEAM - 2026,
Answer: D
The ratio of velocities is 3 : 2.
At perihelion and aphelion the velocity is perpendicular to the radius, and angular momentum is conserved (Kepler's second law).
\[ \begin{aligned} m v_p r_p &= m v_a r_a \\ \frac{v_p}{v_a} &= \frac{r_a}{r_p} = \frac{3}{2} \end{aligned} \]
The planet moves fastest when closest to the sun, so the ratio is the inverse of the distance ratio; 2 : 3 repeats the distances.
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