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The mass of spaceship is 1000kg. It is to be launched from the earth’s surface out into free space. The values of ‘g’ and ‘R’ (radius of earth) are 10m/s² and 6400km respectively. The required energy for this work will be:

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6.4 × 10⁸joules

6.4 × 10¹¹joules

6.4 × 10⁹joules

6.4 × 10¹⁰joules

answer is D.

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Detailed Solution

$\begin{array}{l} E = \frac{1}{2} {mv}_{e}^{2} = \frac{1}{2} m \frac{2 GM}{R} = \frac{mGM}{R} = mgR \\ = 1000 \times 10 \times 64 \times 10^{5} = 6 .4 \times 10^{10} J \end{array}$

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