Question 207: Gravitation

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 ?
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 :-

Accepted Answer

Minimum energy required (E) = Ã¢ÂÂ (Potential energy of
object at surface of earth)
$$ = \left( { - {{GMm} \over R}} ight) = {{GMm} \over R}$$
Now M
earth
= 64 M
moon
$$ho .{4 \over 3}\pi R_e^3 = 64.{4 \over 3}\pi R_m^3$$
$$ \Rightarrow $$ R
e
= 4R
m
Now $${{{E_{moon}}} \over {{E_{earth}}}} = {{{M_{moon}}} \over {{M_{earth}}}}.{{{R_{earth}}} \over {{R_{moon}}}} = {1 \over {64}} 	imes {4 \over 1}$$
$$ \Rightarrow {E_{moon}} = {E \over {16}}$$

Answer

E/32

Answer

E/16

Answer

E/4

Answer

E/64

Gravitation

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