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A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass = 5.98 × 10^24 kg) have to be compressed to be a black hole?

1. 10^−9 m
2. 10^−6 m
3. 10^−2 m
4. 100 m

Correct answer: 10^−2 m

Solution

The Schwarzschild radius (R) is given by R = 2GM/c². Substituting G = 6.67 × 10⁻¹¹ N·m²/kg², M = 5.98 × 10²⁴ kg, and c = 3 × 10⁸ m/s, we get R ≈ 8.87 × 10⁻³ m, which is approximately 10⁻² m.

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