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A mass equal to that of the Earth (6 * 10²⁴ kg) is to be compressed into a sphere such that the escape velocity from its surface equals the speed of light (3 * 10⁸ m/s). What should be the radius of the sphere? (G = 6.67 * 10⁻¹¹ N m² kg⁻²)
- 9 mm
- 8 mm
- 7 mm
- 6 mm
Correct answer: 9 mm
Solution
R = 2GM/c² = 2 * 6.67*10⁻¹¹ * 6*10²⁴ / (9*10¹⁶) = (2 * 6.67 * 6 * 10¹³) / (9 * 10¹⁶) = (80.04 * 10¹³) / (9 * 10¹⁶) = 8.89 * 10⁻³ m ≈ 9 mm.
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