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Physics · Gravitation

JEE Main 2025 — 4 April, Evening Shift — Question 49

An object is kept at rest at a distance of 3R3 R above the earth's surface where RR is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is (Assume MM = mass of earth, G=G= Universal gravitational constant)

  1. Option A:

    2GMR\sqrt{\frac{2 G M}{R}}

  2. Option B:

    GM2R\sqrt{\frac{G M}{2 R}}

    Correct
  3. Option C:

    GMR\sqrt{\frac{G M}{R}}

  4. Option D:

    3GMR\sqrt{\frac{3 G M}{R}}

Answer: B

Step-by-step solution

KEi+PEi=KEg+PEg12mv2−GMm4R=0+0v2=GMR12\begin{aligned} & \mathrm{KE}_{i}+\mathrm{PE}_{i}=\mathrm{KE}_{g}+\mathrm{PE}_{g} \\ & \frac{1}{2} m v^{2}-\frac{\mathrm{GMm}}{4 R}=0+0 \\ & v^{2}=\frac{\mathrm{GM}}{R} \frac{1}{2} \end{aligned} v=GM2Rv=\sqrt{\frac{G M}{2 R}}

figure

Answer key and solution verified before publishing.

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Exam
JEE Main 2025
Paper
4 April, Evening Shift
Subject
Physics
Chapter
Gravitation
Topic
Motion of Satellites and Escape Speed
An object is kept at rest at a distance of 3 R above the earth's… | JEE Main 2025 PYQ with Solution · DhiX AI