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JEE Main 2019 (11 Jan, Shift 1) · Escape Velocity

Escape Velocity question from JEE Main 2019 (11 Jan, Shift 1)

Q64JEE Main 2019 · 11 JAN · SHIFT 1Medium

Escape Velocity

A satellite is revolving in a circular orbit at a height h from the earth's surface, such that h < < R where R is the radius of the earth. Assuming that the effect of earth's atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is:

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Answer: (a)

For $h \ll R$ : orbital speed $v_o = \sqrt{gR}$ .
Escape speed from the same point: $v_e = \sqrt{2gR}$ .
Increase $= \sqrt{2gR} - \sqrt{gR} = \sqrt{gR}(\sqrt{2}-1)$ .
So the answer is (a) $\sqrt{gR}(\sqrt{2}-1)$ .

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