Question 107 of 223

An object is kept at rest at a distance of 3 R above the earth's surface where R is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is :
(Assume $\mathrm{M}=$ mass of earth, $\mathrm{G}=$ Universal gravitational constant)

A$\sqrt{\frac{\mathrm{GM}}{2 \mathrm{R}}}$B$\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}}$C$\sqrt{\frac{3 \mathrm{GM}}{\mathrm{R}}}$D$\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}$

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Answer: (A) $\sqrt{\frac{\mathrm{GM}}{2 \mathrm{R}}}$

$\begin{aligned}
& \mathrm{P}_{\mathrm{P}}+\mathrm{k}_{\mathrm{P}}=\mathrm{P}_{\mathrm{o}}+\mathrm{k}_0 \\
& -\frac{\mathrm{GMm}}{4 \mathrm{R}}+\frac{1}{2} \mathrm{mV}_{\mathrm{P}}^2=0 \\
& \mathrm{~V}_{\mathrm{P}}=\sqrt{\frac{\mathrm{GM}}{2 \mathrm{R}}}
\end{aligned}$
Choice 1