Will the Earth be torn apart by this 10 kg black hole?

No.

The idea of black holes was first hinted at in the 1780s by John Michell as massive “dark stars” from which photons cannot escape. [1] 

About John Michell: He is “a little short man, of black complexion, and fat,” in contemporary accounts. Nonetheless, he is also an  “esteemed a very ingenious Man, and an excellent Philosopher,” who encountered the greatest scientists at that time, such as Benjamin Franklin, Joseph Priestley, and Henry Cavendish at some point in his career.

 Although Michell was wrong about light changing speed due to gravity, we still get a simplified image of a black hole that we found in the universe: a massive, concentrated object with huge gravitational attraction.

However, if we calculate the gravitational acceleration 1mm from the center of a 10 kg black hole, we get g=6.67*10^-4 meters per second squared with direction toward the black hole.

(G is a gravitational constant, the formula is derived from the universal law of gravitation, discovered by Sir Isaac Newton.)

This value is approximately 1/15,000th of the attraction of the Earth ‘s surface. Thus, the attraction is tiny so no one will be influenced. In other words, black holes in the universe tore stars apart by its mass (only the stars with at least 3 times the mass of the Sun can form black holes at the end of their life[2]. ) rather than its name. 

Knowing this, let’s try another simple problem!

Yes, the answer is A.:)

More about masses of black holes see Types – NASA Science.

Could this 10 kg black hole swallow (a part of) the Earth?

No.

Coming to 1916, German physicist Karl Schwarzschild used Einstein’s general theory of relativity to predict “a spherical section of spacetime so badly warped around a concentrated mass that it is invisible to the outside world”[1]. That is, within that spherical space, no matter what you are, you cannot escape from it. Moreover, Schwarzschild concluded that the radius of the “spherical section” (event horizon) is the well-known Schwarzschild radius

where c is the speed of light

Schwarzschild radius can be seen as the “size” of the black hole, and the size of a 10 kg black hole is about 1.5*10^-26 meters. Interestingly, this radius is much smaller than a proton, which means that the 10 kg black hole cannot even swallow an atom.

drawn by Hannah Wang

Will this 10 kg black hole “explode” on the Earth?

It will “explode,” but it will not reach the Earth’s surface.

The Hawking radiation theory was proposed by British physicist Stephen Hawking in 1974. By analysing virtual particle pairs created on two sides of the event horizon, the theory suggests that black holes are not completely “blackbodies”. According to the theory, black holes are emitting particles outward and gradually evaporating. [3]

Let’s calculate some details about the radiation of the 10 kg black hole by the theory.

High temperature: According to Hawking’s radiation theory, the temperature of a black hole is inversely proportional to its mass.

A 10 kg black hole would have an extremely high temperature, around 120 quintillion Kelvin. This high temperature means it emits a large amount of energy in the form of radiation.

High radiation power: The total radiation power

of this 10 kg black hole is about 350 quintillion quadrillion watts. This high-power radiation implies that the black hole is losing mass at an extremely rapid rate.

Rapid mass-energy conversion: All of the black hole’s mass would be converted into energy in an incredibly short time, less than one ten trillionth of a second. Calculated by

When mass is converted into energy, according to Einstein’s famous equation 

a large amount of energy is released. In this case, 900,000,000,000,000,000 joules of energy would be released, which is “similar to approximately 200 million tons of TNT, four times the yield of the largest artificial nuclear explosion (a hydrogen bomb with a yield of 50 million tons).” 

However, the Earth’s atmosphere is huge.

Given the 10kg black hole only exists for one ten trillionth of a second, the “explosion” would occur before the black hole traveled more than 0.025 millimeters (assuming its speed approaches the speed of light). Therefore, unless this 10-kilogram black hole happens to appear in particular places, such as near the surface where humans live or in the ionosphere, its “explosion” would not harm anyone.

What happens if Hawking’s theory is incorrect?

The 10-kilogram black hole would hover above the Earth for a while, following the laws of universal gravitation and laws of mechanics in the presence of Earth’s gravitational field, and eventually fall down and settle near the center of the Earth, growing extremely slowly over billions of years. Meanwhile, the Sun will become larger and larger, the Earth will become hotter and hotter, eventually turning into a barren desert, and then be swallowed by the expanding Sun. By that time, humans had long disappeared. 

The mass of that black hole will still be just a little over 10 kilograms. So, before the extinction of humans, we wouldn’t even notice the existence of this miniature black hole. 

Perhaps it is somewhere right now.

Important source:

https://www.zhihu.com/question/566595314/answer/3048025492

References:

[1]This Month in Physics History | American Physical Society

[2]Black hole | Definition, Formation, Types, Pictures, & Facts | Britannica

[3]Hawking radiation | Black Holes, Quantum Mechanics, Particle Physics | Britannica