Gravitation

JEE Main level, single correct, medium

156 of 223

Question 156 of 223

The mass of a spaceship is 1000 kg1000 \mathrm{~kg}. It is to be launched from the earth's surface out into free space. The value of ' g\mathrm{g} ' and ' RR ' (radius of earth) are 10 m/s210 \mathrm{~m} / \mathrm{s}^2 and 6400 km6400 \mathrm{~km} respectively. The required energy for this work will be ;

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Answer: (D) 6.4×10106.4 \times 10^{10} Joules

To launch the spaceship out into free space, from energy conservation,
−GMmR+E=0\frac{-\mathrm{GMm}}{\mathrm{R}}+\mathrm{E}=0
E=GMmR=(GMR2)mR=mgR\mathrm{E}=\frac{\mathrm{GMm}}{\mathrm{R}}=\left(\frac{\mathrm{GM}}{\mathrm{R}^2}\right) \mathrm{mR}=\mathrm{mgR}
=6.4×1010 J=6.4 \times 10^{10} \mathrm{~J}

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