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The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface 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 is

1. 6.4 × 10¹¹ Joules
2. 6.4 × 10⁸ Joules
3. 6.4 × 10⁹ Joules
4. 6.4 × 10¹⁰ Joules

Correct answer: 6.4 × 10¹⁰ Joules

Solution

Energy to move the ship from the surface to free space equals the binding energy GMm/R = mgR = (1000)(10)(6.4 x 10^6) = 6.4 x 10^10 J.

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