Q140 / 160 · WBJEE 2011 · Physics

If \(\mathrm{g}\) is the acceleration due to gravity on the surface of the earth, the gain in potential energy of an object of mass \(\mathrm{m}\) raised from the earth's surface to a height equal to the radius \(R\) of the earth is

  • A
    \(\frac{\mathrm{mg} \mathrm{R}}{4}\)
  • Correct answer
    B
    \(\frac{m g R}{2}\)
  • C
    \(m g R\)
  • D
    \(2 \mathrm{mg} \mathrm{R}\)

Solution

Hints: \(\Delta \mathrm{U}=\frac{\mathrm{mgh}}{1+\frac{\mathrm{h}}{\mathrm{R}}}=\frac{\mathrm{mgR}}{1+\frac{\mathrm{R}}{\mathrm{R}}}=\frac{\mathrm{mgR}}{2}\)

Hence, the correct answer is option: 'B'.

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