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The mass of a spaceship is $1000 \mathrm{~kg}$. It is to be launched from the earth's surface out into free space. The value of ' $\mathrm{g}$ ' and ' $R$ ' (radius of earth) are $10 \mathrm{~m} / \mathrm{s}^2$ and $6400 \mathrm{~km}$ respectively. The required energy for this work will be ;
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The correct answer is:
$6.4 \times 10^{10}$ Joules
$6.4 \times 10^{10}$ Joules
To launch the spaceship out into free space, from energy conservation,
$\frac{-\mathrm{GMm}}{\mathrm{R}}+\mathrm{E}=0$
$\mathrm{E}=\frac{\mathrm{GMm}}{\mathrm{R}}=\left(\frac{\mathrm{GM}}{\mathrm{R}^2}\right) \mathrm{mR}=\mathrm{mgR}$
$=6.4 \times 10^{10} \mathrm{~J}$
$\frac{-\mathrm{GMm}}{\mathrm{R}}+\mathrm{E}=0$
$\mathrm{E}=\frac{\mathrm{GMm}}{\mathrm{R}}=\left(\frac{\mathrm{GM}}{\mathrm{R}^2}\right) \mathrm{mR}=\mathrm{mgR}$
$=6.4 \times 10^{10} \mathrm{~J}$
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