Verified Solution • 2025–26 Session moderate

QJEEM19Phf208: JEE Main 2019 Physics - Class 11 JEEM19Phf208 Solution: A rocket has to be launched from earth in such a way that it…

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 :-

Multiple Choice Options

  • A E/32
  • B E/16
  • C E/4
  • D E/64

Step-by-Step Verified Solution

Minimum energy required (E) = – (Potential energy of object at surface of earth)

=(−GMmR)=GMmR= \left( { - {{GMm} \over R}} \right) = {{GMm} \over R}

Now Mearth = 64 Mmoon

ρ.43πRe3=64.43πRm3\rho .{4 \over 3}\pi R_e^3 = 64.{4 \over 3}\pi R_m^3

⇒\Rightarrow Re = 4Rm

Now EmoonEearth=MmoonMearth.RearthRmoon=164×41{{{E_{moon}}} \over {{E_{earth}}}} = {{{M_{moon}}} \over {{M_{earth}}}}.{{{R_{earth}}} \over {{R_{moon}}}} = {1 \over {64}} \times {4 \over 1}

⇒Emoon=E16\Rightarrow {E_{moon}} = {E \over {16}}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring