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JEE Main 20254 AprilEvening Shift
Exam
JEE Main
Year
2025
Date
4 April
Shift
Evening Shift
Subject
Physics
Chapter
Gravitation

JEE Main 2025 · 4 April · Evening Shift · Physics · Gravitation

An object is kept at rest at a distance of 3 R above the earth's...

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 M=\mathrm{M}= mass of earth, G=\mathrm{G}= Universal gravitational constant)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

Options

  1. AGM2R\sqrt{\frac{\mathrm{GM}}{2 \mathrm{R}}}
  2. BGMR\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}}
  3. C3GMR\sqrt{\frac{3 \mathrm{GM}}{\mathrm{R}}}
  4. D2GMR\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}

Correct answer

A. GM2R\sqrt{\frac{\mathrm{GM}}{2 \mathrm{R}}}

Step-by-step solution

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
<br/>PP+kP=Po+k0−GMm4R+12mVP2=0 VP=GM2R<br/>\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
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