Q68 / 90 · JEE Main 2012 (Offline) · Physics

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 ;

  • A
    $6.4 \times 10^{11}$ Joules
  • B
    $6.4 \times 10^8$ Joules
  • C
    $6.4 \times 10^9$ Joules
  • Correct answer
    D
    $6.4 \times 10^{10}$ Joules

Solution

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

Hence, the correct answer is option: 'D'.

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