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NEET 2013
Exam
NEET
Year
2013
Subject
Physics
Chapter
Gravitation

NEET 2013 · Physics · Gravitation

A particle of mass ' m ' is kept at rest at a height 3 R from the...

A particle of mass ' mm ' is kept at rest at a height 3R3 R from the surface of earth, where ' RR ' is radius of earth and ' MM ' is mass of earth. The minimum speed with which is should be projected, so that it does not return back, is (g(g is acceleration due to gravity on the surface of earth)

Options

  1. A(GM2R)1/2\left(\frac{G M}{2 R}\right)^{1 / 2}
  2. B(gR4)1/2\left(\frac{g R}{4}\right)^{1 / 2}
  3. C(2gR)1/2\left(\frac{2 g}{R}\right)^{1 / 2}
  4. D(GMR)12\left(\frac{G M}{R}\right)^{\frac{1}{2}}

Correct answer

A. (GM2R)1/2\left(\frac{G M}{2 R}\right)^{1 / 2}

Step-by-step solution

Escape velocity Ve=2GM(R+h)V_e=\sqrt{\frac{2 \mathrm{GM}}{(\mathrm{R}+h)}} from the question h=3Rh=3 R∴Ve′=2GMR+3R=2GM4R=GM2R=gR2 where g=GMR2\begin{aligned}& \therefore V_e^{\prime}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}+3 \mathrm{R}}}\\ & =\sqrt{\frac{2 G M}{4 R}}=\sqrt{\frac{G M}{2 R}}=\sqrt{\frac{g R}{2}}\\ & \text{ where }g=\frac{G M}{R^2} \end{aligned}$$
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