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(D) The energy required to launch a body of mass $m$ from the earth's surface to infinity is equal to the binding energy of the body at the earth's su

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$6.4	imes10^{10}\,J$

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(D) The energy required to launch a body of mass $m$ from the earth's surface to infinity is equal to the binding energy of the body at the earth's surface.$W = U_{final} - U_{initial} = 0 - \left(-\frac{GMm}{R}ight) = \frac{GMm}{R}$Since $g = \frac{GM}{R^2}$,we have $GM = gR^2$.Substituting this into the expression for work:$W = \frac{(gR^2)m}{R} = mgR$Given values: $m = 1000\,kg$,$g = 10\,m/s^2$,$R = 6400\,km = 6400 	imes 10^3\,m$.$W = 1000 	imes 10 	imes 6400 	imes 10^3$$W = 64 	imes 10^9\,J$$W = 6.4 	imes 10^{10}\,J$

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

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