[John369 (OP)]

Suppose some future technology is able to create a black hole. And they managed to create a tiny black hole with 10 times the mass of earth. How long would the black hole take to reach the earth's core and start eating up the planet from inside? And how to calculate this? And would this happen at all? What would happen when a tiny black hole gets formed on the surface of planet earth? Would it also produce earthquake? If so, what magnitude on the Richter scale? And how to comprehend 5e+17 m/s^2 surface gravity? And 4.1e+67 entropy?

[Halc]

Suppose some future technology is able to create a black hole. And they managed to create a tiny black hole with 10 times the mass of earth. How long would the black hole take to reach the earth's core and start eating up the planet from inside?

To have 10 times the mass of Earth, future technology would need to find a way to transport that sort of mass here from wherever they got it.  It would start 'eating' stuff immediately and would not need to get to Earth's core (or better put, Earth's core would not need to get to it) before that started happening.

I thought from the title that you were positing a small black hole, say produced in a particle accelerator.  Such an entity would not mass more than a few subatomic particles.  The thing you describe is totally massive, nearly that of Uranus.

And would this happen at all? What would happen when a tiny black hole gets formed on the surface of planet earth?

Earth would be on the surface of the black hole, and yes, it would fall in, just like it would if you dropped it on Uranus. Not all of it, or even most of it necessarily, since much mass would orbit into a sort of accretion disk and be ejected away even.  Nothing recognizable would be left of Earth though.

Would it also produce earthquake? If so, what magnitude on the Richter scale?

I don't think there would be a Earth sticking around long enough to quake.

[evan_au]

I thought from the title that you were positing a small black hole, say produced in a particle accelerator.

To add to what Halc said, this was a genuine concern expressed by some people before the Large Hadron Collider turned on.

For the LHC to form such a black hole, there would need to be some deviation from General Relativity on very tiny scales - such as if gravity can "leak" into more than 3 dimensions, weakening the energy needed to form a black hole. But even if such deviations existed, cosmic rays have been slamming into the Moon for billions of years, at much higher energy than the LHC can achieve - and the Moon is still there.

Another possibility is micro-black holes, with the mass of a mountain or larger, left over from the Big Bang. If one of these hit the Earth with the usual meteorite velocity of 15-30 km/second, it would pass straight through the Earth in about 5 minutes. It would collect some of Earth's matter as it did so - but not enough to slow down the black hole significantly, or enough to collapse the Earth.
- If it hit someone in a critical organ it might kill or injure them.
- It might make a bang as it disturbed the atmosphere, but I suspect it would be softer than thunder.

See: https://en.wikipedia.org/wiki/Micro_black_hole

[Halc]

Another possibility is micro-black holes, with the mass of a mountain or larger, left over from the Big Bang. If one of these hit the Earth with the usual meteorite velocity of 15-30 km/second, it would pass straight through the Earth in about 5 minutes. It would collect some of Earth's matter as it did so - but not enough to slow down the black hole significantly, or enough to collapse the Earth.
- If it hit someone in a critical organ it might kill or injure them.
- It might make a bang as it disturbed the atmosphere, but I suspect it would be softer than thunder.

I took the mass of mt. Everest (taken from quora, so buyer beware) of 1.6e14 kg or 60 billion cubic meters which yields a Schwarzschild diameter of around 5 picometers if I did my math right.  Anything that gets fairly close to it gets sucked in, but needs to do so quickly as it passes by.  So maybe it absorbs a cylinder of material of just just say 5e-23 square meters in cross section.
What is the volume of that cylinder?  Not much.  1.1e7 meters in length if it hits Earth centered makes for a volume of 5.5e-16 cubic meters which masses well under a gram.  No, the fairly slow moving primordial black hole isn't going to slow down due to smacking into that much mass.  It just keeps right on going.

I think I can personally survive a hole like that passing through me, no matter how critical the organ.  15 km/sec is still a dang fast bullet, leaving no time to linger and take more material.

[evan_au]

a tiny black hole gets formed on the surface of earth

A bigger risk than a fast-moving micro-black hole is a slow-moving black hole, for example if it were formed in a lab on the Earth's surface. In this case it would go into an elliptical orbit around the center of the Earth, with an orbital period of under an hour. It would continually gain mass (at a slow rate), and would periodically appear at or near the surface of the Earth, at roughly the altitude it was created.

This would slowly increase in mass, which means it would grow more quickly. Eventually, it would leave a trail of destruction behind it, big enough to kill a person, collapse a building, and be picked up on seismographs. Eventually, it would eat the Earth, but we would get some warning.

A somewhat different fate would occur if the micro black hole was so small that it "evaporated" via Hawking radiation faster than it was absorbing mass from the Earth. This would leave a burning path through the Earth, ending with a subatomic explosion that would certainly be detected by seismometers looking for nuclear tests. But with a location probably well below the crust of the Earth, it would quickly be ruled out as a nuclear test.