A black hole is an object whose gravitational field is so strong that even light cannot escape. To what approximate radius would Earth (mass = 5.98 × 1024 kilograms) have to be compressed in order to become a black hole?
A. 1 nm
B. 1 µm
C. 1 cm
D. 100 m
E. 10 km
(GR9677 #67)
Solution:
Schwarzschild radius: GMm/R = ½ mc2
→ R = 2GM/c2
G = 6.67 × 10−11 m3/(kg·s2)
M = 5.98 × 1024 kg
c = 3 × 108 m/s
R = 2 (6.67 × 10−11)(5.98 × 1024) / (3 × 108)2
= (2·6.67·5.98 / 9) × 10−11× 1024 × 10−16
≈ (2·7·6 / 9) × 10−3 ≈ 1 cm
Answer: C
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