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Question:

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?

E32

E4

E16

E64

Solution:

Correct option is B. E/16
minimum energy required (E) = -(Potential energy of object at surface of earth) - (-GMm/R) = GMm/R
Now Mearth = 64Mmoon
ρ. (4/3)πRe3 = 64. (4/3)πRm3 ⇒ Rr = 4Rm
Now Emoon/Eearth = (Mmoon/Mearth) * (Rearth/Rmoon) = (1/64) * (4/1)
Emoon = E/16