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JEE Main 2021 (25 Jul, Shift 1) · Kepler's Laws & Planetary Motion

Kepler's Laws & Planetary Motion question from JEE Main 2021 (25 Jul, Shift 1)

Q19JEE Main 2021 · 25 JUL · SHIFT 1Medium

Kepler's Laws & Planetary Motion

The minimum and maximum distances of a planet revolving around the sun are x1 and x2. If the minimum speed of the planet on its trajectory is v0 then its maximum speed will be:

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Answer: (d)

Angular momentum is conserved: $v_{max}\,x_{min} = v_{min}\,x_{max}$ .
Maximum speed is at minimum distance $x_1$ ; minimum speed $v_0$ is at $x_2$ .
$v_{max}\,x_1 = v_0\,x_2 \Rightarrow v_{max} = \frac{v_0 x_2}{x_1}$
So the answer is (d) $\frac{v_0x_2}{x_1}$ .

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