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 :
\(6.4 \times 10^{10}\text{ Joules}\)
\(6.4 \times 10^{11}\text{ Joules}\)
\(6.4 \times 10^8\text{ Joules}\)
\(6.4 \times 10^9\text{ Joules}\)
Solution:
The minimum energy required to escape the earth's gravitational pull from the surface is \(E = \frac{GMm}{R} = mgR\). Substituting \(m = 1000\text{ kg}\), \(g = 10\text{ m/s}^2\), and \(R = 6.4 \times 10^6\text{ m}\), we find \(E = 6.4 \times 10^{10}\text{ Joules}\).
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