The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface out into free space. The value of g and R (radius of earth) are 10 m/s² and 6400 km respectively. The required energy for this work will be: (a) 6.4 × 10¹¹ Joules (b) 6.4 × 10⁸ Joules (c) 6.4 × 10⁹ Joules (d) 6.4 × 10¹⁰ Joules

Answer: (d). Energy to send a body from the surface to free space: E = GMm/R = mgR. E = 1000×10×6.4×10⁶. E = 6.4×10¹⁰ J. So the answer is (d) 6.4×10¹⁰ Joules.

The mass of a spaceship is 1000 kg. It is to be launched from the… | JEE Main 2012 (AIEEE)

Q73JEE Main 2012 · AIEEEMedium

Escape Velocity

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

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Answer: (d)

Energy to send a body from the surface to free space: $E = \frac{GMm}{R} = mgR$ .
$E = 1000\times10\times6.4\times10^{6}$ .
$E = 6.4\times10^{10}$ J.
So the answer is (d) $6.4\times10^{10}$ Joules.

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