An object of mass 1 kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [If, $\mathrm{g}=10 \mathrm{~ms}^{-2}$ and radius of earth $=6400 \mathrm{~km}$ ]
Select the correct option:
A
48 MJ
B
24 MJ
C
36 MJ
D
12 MJ
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
$\begin{aligned} & U_i=\frac{-G M m}{R} \\ & U_f=-\frac{G M m}{4 R} \\ & \Delta U=U_f-U_i=\frac{3 G M m}{4 R}=\frac{3}{4} \mathrm{mgR} \\ & =\frac{3}{4} \times 1 \times 10 \times 64 \times 10^5 \\ & =48 \mathrm{MJ}\end{aligned}$
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