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)

• Correct answer
  A

  $\sqrt{\frac{\mathrm{GM}}{2 \mathrm{R}}}$
• B

  $\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}}$
• C

  $\sqrt{\frac{3 \mathrm{GM}}{\mathrm{R}}}$
• D

  $\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}$

Solution

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

Hence, the correct answer is option: 'A'.