Q150 / 160 · WBJEE 2010 · Physics

The change in the gravitational potential energy when a body of mass $m$ is raised to a height $n \mathrm{R}$ above the surface of the Earth is (here $R$ is the radius of the Earth)

  • Correct answer
    A
    $\left(\frac{n}{n+1}\right) m g \mathrm{R}$
  • B
    $\left(\frac{n}{n-1}\right) m g \mathrm{R}$
  • C
    $n m g R$
  • D
    $\frac{m g R}{n}$

Solution

Hints: $\Delta \mathrm{U}=\frac{m g h}{1+\frac{h}{\mathrm{R}}}=\frac{m g \times n \mathrm{R}}{1+\frac{n \mathrm{R}}{\mathrm{R}}}=\frac{n m g \mathrm{R}}{n+1}$

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

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