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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
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a height \( h \) before returning to earth. At height \( h \) a
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body is thrown from the rocket with speed \( v_{0} \) in such 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 value of \( h \) is
(1) \( 1.5 \times 10^{5} \mathrm{~m} \)
(2) \( 3.2 \times 10^{5} \mathrm{~m} \)
(3) \( 3.2 \times 10^{10} \mathrm{~m} \)
(4) \( 1.6 \times 10^{6} \mathrm{~m} \)


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