A rocket is fired vertically upwards with a speed of \( \mathrm{v}\left(=5 \mathrm{kms}^{-1}\right) \) from the surface of earth. It goes up to a height \( h \) before returning to earth. At height \( h \) a body is thrown from the rocket with speed \( v_{0} \) in such
\( \mathrm{P} \)
a way so that the body becomes a satellite of earth. Let the mass of the earth, \( M=6 \times 10^{24} \mathrm{~kg} \); mean radius of the earth,
\[
\begin{array}{l}
\mathrm{R}=6.4 \times 10^{6} \mathrm{~m} ; \\
\mathrm{G}=6.67 \times 10^{-11} \mathrm{Nm}^{2} \mathrm{~kg}^{-2} ; \\
\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}
\end{array}
\]
The energy to be spent in taking the satellite out of the gravitational field of the earth is (mass of the satellite is \( 200 \mathrm{~kg} \) )
(1) \( 5.0 \times 10^{9} \mathrm{~J} \)
(2) \( 10.0 \times 10^{9} \mathrm{~J} \)
(3) \( 2.5 \times 10^{9} \mathrm{~J} \)
(4) \( 5.0 \times 10^{6} \mathrm{~J} \)
0