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Question:

Block hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass=5.98×10²⁴kg) have to be compressed to be a black hole?

10⁻¹⁵m

10⁻¹⁶m

10⁻¹⁴m

100m

Solution:

Light is unable to escape so Ve=C √(2GM/R) = 3×10⁸ m/s => R ≈ 2GM/C² ≈ 2 × (6.67×10⁻¹¹ N⋅m²/kg²) × (6×10²⁴ kg) / (3×10⁸ m/s)² ≈ 9 mm ≈ 10⁻⁵ m ≈ 10⁻¹⁶m