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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 = $5.98\times10^{24}$ kg) have to be compressed to be a black hole?
A
$10^{-9}$ m
B
$10^{-6}$ m
C
$10^{-2}$ m
D
100 m
Detailed Solution
Escape velocity $= \sqrt{\frac{2GM}{R}} = c$ (speed of light)
$R = \frac{2GM}{c^2} = \frac{2\times 6.6\times10^{-11}\times 5.98\times10^{24}}{(3\times10^8)^2}$ m
$R \approx 10^{-2}$ m
$R = \frac{2GM}{c^2} = \frac{2\times 6.6\times10^{-11}\times 5.98\times10^{24}}{(3\times10^8)^2}$ m
$R \approx 10^{-2}$ m