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NEET 2013
Exam
NEET
Year
2013
Subject
Physics
Chapter
Gravitation

NEET 2013 · Physics · Gravitation

A body of mass m taken from the earth's surface to the height equal...

A body of mass mm taken from the earth's surface to the height equal to twice the radius (R)(R) of the earth. The change is potential energy of body will be

Options

  1. Amg2Rm g 2 R
  2. B23mgR\frac{2}{3} m g R
  3. C3mgR3 \mathrm{mgR}
  4. D13mgR\frac{1}{3} m g R

Correct answer

B. 23mgR\frac{2}{3} m g R

Step-by-step solution

Change in potential energy ΔU=−GMmR+2R−(−GMmR)=−GMm3R+GMmR=2GMm3R=23mgR[∵g=GMR2]\begin{aligned} \Delta U & =-\frac{G M m}{R+2 R}-\left(-\frac{G M m}{R}\right) \\ & =-\frac{G M m}{3 R}+\frac{G M m}{R} \\ & =\frac{2 G M m}{3 R}=\frac{2}{3} m g R \quad\left[\because g=\frac{G M}{R^2}\right] \end{aligned}
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