A rocket has to be launched from earth in such a way that it never… | JEE Main 2019 (8 Apr, Shift 2)

Q62JEE Main 2019 · 8 APR · SHIFT 2Medium

Escape Velocity

A rocket has to be launched from earth in such a way that it never returns. If E is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have if the same rocket is to be launched from the surface of the moon? Assume that the density of the earth and the moon are equal and that the earth's volume is 64 times the volume of the moon :-

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Answer: (b)

Minimum launch energy $E = \frac{GMm}{R}$ ; with equal density $M \propto R^3$ , so $E \propto R^2$ .
$V_E = 64V_M \Rightarrow R_E = 4R_M$ .
$E_{moon} = \frac{E}{4^2} = \frac{E}{16}$ .
So the answer is (b) $E/16$ .

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Escape Velocity question from JEE Main 2019 (8 Apr, Shift 2)

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