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JEE Main 2023 (30 Jan, Shift 2) · Escape Velocity

Escape Velocity question from JEE Main 2023 (30 Jan, Shift 2)

Q36JEE Main 2023 · 30 JAN · SHIFT 2Medium

Escape Velocity

An object is allowed to fall from a height $R$ above the earth, where $R$ is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be

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Answer: (b)

Released at $2R$ from the centre: $\frac{1}{2}v^2 = GM\left(\frac{1}{R} - \frac{1}{2R}\right) = \frac{GM}{2R}$ .
$v^2 = \frac{GM}{R} = gR$ .
So the answer is (b) $\sqrt{gR}$ .

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