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JEE Main 2021 (31 Aug, Shift 1) · Escape Velocity

Escape Velocity question from JEE Main 2021 (31 Aug, Shift 1)

Q53JEE Main 2021 · 31 AUG · SHIFT 1Difficult

Escape Velocity

The masses and radii of the earth and moon are (M1, R1) and (M2, R2) respectively. Their centres are at a distance 'r' apart. Find the minimum escape velocity for a particle of mass 'm' to be projected from the middle of these two masses:

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Answer: (b)

At the midpoint: $V = -\dfrac{2GM_1}{r} - \dfrac{2GM_2}{r} = -\dfrac{2G(M_1+M_2)}{r}$ .
$v^2 = 2|V| = \dfrac{4G(M_1+M_2)}{r}$
So the answer is (b) $V = \sqrt{\dfrac{4G(M_1+M_2)}{r}}$ .

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