A tiny black hole resides inside ping-pong ball submerged in water?

Question

Mass of the black hole is M = 10^12 kg.
Such black hole has radius about the size of a proton,
and it behaves as Newtonian point mass at inter-atomic,
and larger distances.

The black hole resides inside vacuumized ping-pong ball of
radius R = 2cm at distance D = 1 cm from the center of the ball.
A bucketful of water is hold around the ball by the pull of gravity of the black hole, and asumed its equilibrium shape.

What is the force of buoyancy excerted by water on the ball?

Answer 1

interesting question.

but it seems to me that 10^12 kg is quite heavy, the ping pong ball would collapse even though it is outside of the event horizon. then the water would come in and further feed the black hole.

i think even the bucket that it was in would be crushed. but that might be all. the black hole would sit at the bottom of the bucket slowly sucking away the air and growing until it can crush the bucket then if there is anything else near it they could be sucked in, and the air would continually be sucked in. eventually such a black hole could destroy earth.

umm, as for the buoyancy, the ball would sink, 10^12 kg in the size of a ping pong ball would certainly be more than the density of water, so the ball would sink, assuming nothing collapses.

Answer 2

The force water exerts is exactly equal to the weight of the water being displaced by the object. So it doesn't matter whether the ping pong ball is empty or weighs 10^12 kg. It displaces 4/3pi(r^3) of water, and water has a density of 1g/cm^3. So it will displace 4/3*pi*8 cm^3. This should also be its mass in grams.
To get its weight in newtons (and therefore find the force of the buoyancy), you need to multiply this by 1000 and the water's acceleration due to gravity (f=ma). This should be G*mass of black hole/(.01 m)^2.(g=Gm/r^2)
So I have no idea what these numbers turn out to be, but that's the method I came up with. I'm kind of assuming that density does NOT change with increased gravity and that it's more of a introductory physics problem. Hope it works out.

Edit: Nevermind, it's 0. The force it's exerting is equal in all directions.

Answer 3

An interesting thought problem. Given that there is no force acting to suspend the mass of the black hole in the center of the ping pong ball.

One thing you have to do is to remove the influence of other gravitational fields. Otherwise the mass would quickly fall to the bottom of the pail and consume the ball, water and bucket.

In any system the downward pressure of the mass would far exceed the negative effect of buoyancy. You could calculate the displaced mass of water dictated by the volume of the ball. It is insignificant when compared to the mass of the black hole.

Answer 4

I assume that the water is incompressible and that the gravitational field of the blackhole has no effect on the water. If this assumption is correct, the buoyancy will be exactly the same as the buoyancy exerted on a normal ping-pong ball of the same diameter.

If the density of water has gone up because of the gravitational pull of the mini-blackhole, the buoyanct also goes up. By how much, I have no idea.

Answer 5

In fact, there would be no buoyancy. Even at that infintesimal amount of mass, the black hole actually consumes the ball and the event horizon grows as the mass expands to encompass the surrounding water.

Answer 6

confident monkey interior the midsection with a compelled rite to introduce the nut sucking monkey vs. guy mayhem. Or a minimum of that's how i could react to the situation. at the start, wreck the ping pong balls. i'm sorry, yet they must circulate. Secondly, your buddy's automobile is on hearth. positioned that sh*t out with a paddle and a few pumpkin juice. finally, i'm sorry, yet your paraplegic chum, Paula, exceeded directly to the finished beyond mutually as pooping on a piano in the past Pope Peter's ***** social gathering.

Answer 7

This is a nonsense question not worth any time spent on it.

Answer 8

for me it's impossible (i didn't read the paragraph)
ps. i teach at caltech