JEE Mains · Physics · STD 11 - 7. gravitation
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 \(\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}\)
Answer & Solution
Correct Answer
(A) \(\sqrt{\frac{\mathrm{GM}}{2 \mathrm{R}}}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \mathrm{P}_{\mathrm{P}}+\mathrm{k}_{\mathrm{P}}=\mathrm{P}_{\mathrm{o}}+\mathrm{k}_0 \\ & -\frac{\mathrm{GMm}}{4 \mathrm{R}}+\frac{1}{2} \mathrm{mV}_{\mathrm{P}}^2=0 \\ & \mathrm{~V}_{\mathrm{P}}=\sqrt{\frac{\mathrm{GM}}{2 \mathrm{R}}} \end{aligned}\) Choice 1
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