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Say a black hole with the diameter of around 200 meters or so was formed on the Earth's surface, how much damage would it cause?

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  • $\begingroup$ That would be a black hole with the mass of a small star. Where would the mass come from? Irrespective of that, there wouldn't be an earth after about 5 seconds, or so, and the black hole would have increased in diameter by about 9mm, I believe. $\endgroup$ – CuriousOne Jan 1 '16 at 8:25
  • $\begingroup$ On second thought, the actual accretion may be much smaller than the total mass of the planet and most of the matter might actually escape in form of jets... one would have to look at actual simulations of the accretion process near the Schwarzschild radius. $\endgroup$ – CuriousOne Jan 1 '16 at 8:53
  • $\begingroup$ A black hole the mass of the Earth is about the size of a ping pong ball, so your black hole would be over 10,000 Earth masses. That much mass, even on the far side of the Earth, we'd experience over 2,500 G forces, enough to crumble every building and kill every living thing except, perhaps, bacteria & viruses and that's on the farthest part of the earth from the hole. The nearest parts of the Earth, the effects would be almost like pure energy, hotter than the inside of the sun as the earth was quickly torn into an accretion disk shooting radiation out of the poles of the disk. $\endgroup$ – userLTK Jan 1 '16 at 8:54
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    $\begingroup$ So, on a destructiveness scale 1-10, I'd rate that one about a 15. $\endgroup$ – userLTK Jan 1 '16 at 8:55
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The radius of a black hole (the Schwarzschild radius) is given by:

$$ r_s = \frac{2GM}{c^2} $$

so the mass of your 100 metre radius black hole would be:

$$ M = \frac{r_s c^2}{2G} \approx 6.75 \times 10^{28}\,\text{kg} $$

This is about 30 times the mass of Jupiter. A mass that big approaching the Earth would rip it to pieces due to tidal forces before the two bodies made contact. The fact the mass was a black hole would be irrelevant as far as all (shortly to be extinct) life on Earth was concerned.

For the effect of a more sensibly sized black hole see How fast a (relatively) small black hole will consume the Earth?.

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