Q133 / 160 · AP EAMCET 2024 (22 May Shift 2) · Physics

The gravitational potential energy of a body on the surface of the earth is E. If the body is taken from the surface of the earth to a height equal to $150 \%$ of the radius of the earth, its gravitational potential energy is

  • Correct answer
    A
    0.4 E
  • B
    0.2 E
  • C
    0.6 E
  • D
    0.3 E

Solution

$\mathrm{E}=\frac{-\mathrm{GMm}}{\mathrm{R}}, \mathrm{h}=1.5 \mathrm{R}$ $\begin{aligned} & \therefore \quad \mathrm{R}^{\prime}=(\mathrm{R}+\mathrm{h})=(\mathrm{R}+1.5 \mathrm{R})=2.5 \mathrm{R} \\ & \therefore \quad \mathrm{E}^{\prime}=-\frac{\mathrm{GMm}}{\mathrm{R}^{\prime}}=-\frac{\mathrm{GMm}}{2.5 \mathrm{R}}=\frac{1}{2.5}\left(-\frac{\mathrm{GMm}}{\mathrm{R}}\right) \\ & \therefore \mathrm{E}^{\prime}=\frac{\mathrm{E}}{2.5}=0.4 \mathrm{E}\end{aligned}$

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

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