A rocket has to be launched from earth in such a way that it never returns. If E is the minimum energy…

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.
  1. E64
  2. E4
  3. E32
  4. E16

Solution

Mearth=64 Mmoon and Rearth=4 Rmoon
Given: E=G MearthmRearth
Now, for the moon,

 E'=G MmmRm
=GMearth64 mRearth4=G Mearth m16 Rearth=E16

Asked in: JEE Main 2019 (08 Apr Shift 2)

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