The mass of a spherical planet is 4 times the mass of the earth, but its radius (R) is same as that of the…

The mass of a spherical planet is 4 times the mass of the earth, but its radius (R) is same as that of the earth. How much work is done in lifting a body of mass $5 \mathrm{~kg}$ through a distance of $2 \mathrm{~m}$ on the planet? $\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$
  1. $400 \mathrm{~J}$
  2. $200 \mathrm{~J}$
  3. $800 \mathrm{~J}$
  4. $300 \mathrm{~J}$

Solution

$\begin{aligned} & \mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}^2}, \mathrm{~g}^{\prime}=\frac{\mathrm{GM}^{\prime}}{\mathrm{R}^2}=\frac{\mathrm{G} \times 4 \mathrm{M}}{\mathrm{R}^2}=4 \mathrm{~g} \\ & \mathrm{~W}=\mathrm{mg} \mathrm{h}=4 \mathrm{mgh}=4 \times 5 \times 10 \times 2=400 \mathrm{~J}\end{aligned}$ ~

Asked in: MHT CET 2021 (23 Sep Shift 2)

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