MHT CET · Physics · Gravitation
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? \(\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)\)
- A \(400 \mathrm{~J}\)
- B \(200 \mathrm{~J}\)
- C \(800 \mathrm{~J}\)
- D \(300 \mathrm{~J}\)
Answer & Solution
Correct Answer
(A) \(400 \mathrm{~J}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}^2}, \mathrm{~g}^{\prime}=\frac{\mathrm{GM}^{\prime}}{\mathrm{R}^2}=\frac{\mathrm{G} \times 4 \mathrm{M}}{\mathrm{R}^2}=4 \mathrm{~g} \\ & \mathrm{~W}=\mathrm{mg} \mathrm{h}=4 \mathrm{mgh}=4 \times 5 \times 10 \times 2=400 \mathrm{~J}\end{aligned}\)
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