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JEE Main 2016 · Escape Velocity

Escape Velocity question from JEE Main 2016

Q68JEE Main 2016Medium

Escape Velocity

A satellite is revolving in a circular orbit at a height $'h'$ from the earth's surface (radius of earth $R;\ h << R$ ). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to: (Neglect the effect of atmosphere.)

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Answer: (d)

For $h \ll R$ : $v_o = \sqrt{gR}$ and $v_e = \sqrt{2gR}$ at that point.
Minimum increase $= \sqrt{2gR} - \sqrt{gR} = \sqrt{gR}(\sqrt{2}-1)$ .
So the answer is (d) $\sqrt{gR}(\sqrt{2}-1)$ .

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