# A rocket has to be launched from earth in such a way that it never returns. If E is the minimum energy that the launcher should  have if the same rocket is to be lunched 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.Option 1)$\frac{E}{64}$Option 2)$\frac{E}{32}$Option 3)$\frac{E}{4}$Option 4)$\frac{E}{16}$

Given:

$\rho _{moon}=\rho _{earth}$

Volume of Earth=64(volume of moon)

$\frac{mass\;of\;earth}{mass\;of\;moon}=\frac{\frac{4}{3}\pi R_{e}^{3} \times \rho _{earth}}{\frac{4}{3}\pi R_{m}^{3} \times \rho _{moon}}=\frac{R_{e}^{3}}{R_{m}^{3}}=64$

$R_{e}=4R_{m} \;\;and \;\; M_{e}=64M_{m}$

$\frac{E_{earth}}{E_{moon}}=\frac{\frac{GM_{e}m}{R_{e}}}{\frac{GM_{m}m}{R_{m}}}=\frac{M_{e}}{M_{m}}\times \frac{R_{m}}{R_{e}}=64 \times \frac{1}{4}=16$

$E_{moon}=\frac{E_{earth}}{16}$

Option 1)

$\frac{E}{64}$

Option 2)

$\frac{E}{32}$

Option 3)

$\frac{E}{4}$

Option 4)

$\frac{E}{16}$

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