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The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is $v$. For a satellite orbiting at an altitude of half of the earth's radius, the orbital velocity is
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The correct answer is:
$\sqrt{\frac{2}{3}} v$
$v=\sqrt{\frac{G M}{R+h}}$
For first satellite $h=0$,
$v_1=\sqrt{\frac{G M}{R}}$
$\begin{aligned}& \text { For second satellite } h=\frac{R}{2}, \quad v_2=\sqrt{\frac{2 G M}{3 R}} \\& v_2=\sqrt{\frac{2}{3}} v_1=\sqrt{\frac{2}{3}} v\end{aligned}$
For first satellite $h=0$,
$v_1=\sqrt{\frac{G M}{R}}$
$\begin{aligned}& \text { For second satellite } h=\frac{R}{2}, \quad v_2=\sqrt{\frac{2 G M}{3 R}} \\& v_2=\sqrt{\frac{2}{3}} v_1=\sqrt{\frac{2}{3}} v\end{aligned}$
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