The planet Mars may be considered to be an isolated sphere of radiu...

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The planet Mars may be considered to be an isolated sphere of radius \( 3.395 \times 10^{6} \mathrm{~m} \) with its mass of \( 6.42 \times 10^{23} \mathrm{~kg} \) concentrated at its centre. A rock of mass \( \mathbf{1} \cdot 40 \mathrm{~kg} \) rests on the surface of Mars.

For this rock, show that its gravitational potential energy is \( -1 \cdot 77 \times 10^{7} \mathrm{~J} \).
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