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What would happen to to a planet 10 times the size of Jupiter, if there was a black hole the size of a golf ball in the core of the planet?
Would the planet be eaten by the black hole?
Or would the planet destroy the black hole?
Or do you think something else would happen?
The radius of a golf ball is a little over $20\;\text{mm}$. Let's use $20\;\text{mm}$ exactly. Rearranging the formula for the Schwarzchild radius,
$R_{Sch} = \frac{2\text{G}M}{\text{c}^{2}}$
$M = \frac{R_{Sch}\cdot \text{c}^{2}}{2\text{G}}$
we get the mass of your black hole as $1.35\cdot10^{25}\;\text{kg}$, $2.25$ times the mass of Earth, but $1\%$ of Jupiter. That's much too large for any significant Hawking evaporation.
So your planet is toast. There's no way that a planet can destroy a black hole of any size - Hawking evaporation is the only way to do it. It will rapidly fall into the black hole and become part of it, liberating a lot of energy in the process. The exact mechanics will depend on whether the black hole is charged and/or rotating, but I would expect it to take a few years, and I wouldn't want to be in the same stellar neighbourhood while it was happening. The more it eats, the bigger it gets, and the faster it eats the rest. The hole will end up with $10.01$ times the mass of Jupiter, and will now have a radius of around $28\;\text{m}$. It will eventually evaporate after $1.86\cdot10^{58}$ years.
(disclaimer: I am not an astrophysicist, so take the accuracy with a grain of salt)
While the black hole will have gravity on its own, the real effect of its existence is that there will be a region in Jupiter's core that can no longer support the planet above it, and so Jupiter will begin to collapse under its own weight.
Now, Jupiter is really big, and the black hole is a tiny target — while the core will probably be compressed into the hole, the outer layers will most likely fall and "miss", forming a hot dust cloud orbiting the hole with jets of high energy gasses ejected.
In the worst case scenario, the pressures nearest the black hole are enough to ignite fusion, and the continued collapse makes Jupiter go supernova.
Now I too am curious about what could really happen.
It doesn't matter if the black hole is rotating, since Jupiter is already rotating. Since Jupiter's mass already has a rotational moment of inertia, it will continue spinning as it is sucked in.
Also, conceptually, the total mass of Jupiter has not changed by very much by introducing a black hole, so there is almost no additional sucking force that is pulling Jupiter's mass into the center.
Since the surface area of the black hole is so small (0.005 m^2, at least at first), you won't actually be losing that much mass, relative to the entire mass of Jupiter. So the loss of mass won't be that fast.
Jupiter isn't collapsing right now because the force of gravity is being counteracted by the pressure of the particles that are already in the center. As those particles interact with the event horizon and 'dissapear', other particles will move to take their place. However, consider that if you divide Jupiter into an infinite set of spheres, nested one inside the other, the spheres get larger as you go towards the surface. Therefore, as mass is lost to the black hole, the mass being sucked inwards will be compressed and heated. This heating will in turn increase the pressure in the regions near the black hole, and will thus slow the rate of collapse of the planet.
None of these considerations really change the outlook for the planet, as Mike Scott put it, but the planet will die a spinning, glowing white hot death, as opposed to just imploding.
