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To disassemble the Earth completely, scattering all of its mass to infinity, the energy that must be supplied equals x * G M² / (5 R), where M and R are the Earth's mass and radius and G is the gravitational constant. Find the integer value of x (round to the nearest integer).
- 1
- 2
- 3
- 4
Correct answer: 3
Solution
The gravitational self-energy of a uniform sphere is -(3/5) G M² / R. The energy needed to take all mass to infinity is the magnitude of this, so x = 3.
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