I find it very easy to solve some of these physics questions by thinking about a degenerate version of it instead, with exaggerated parameters (since these physics phenomenons are described by continuous/monotonic functions).
So for the bowling ball, I replace it with an imaginary marble weighing 1 ton and the answer is now self-evident.
That’s exactly the path I would have gone, ask clarifying question to confuse the interviewers:
- Is my boat actually floating in the lake?
- Is the lake filled with water?
- If yes, what is the temperature gradient of that water from top to bottom?
- How deep is the lake at the spot the ball is dropped?
- What is the current time and phase of the moon, and what are the exact coordinates of the ball drop?
- Are we doing this during some « end of the world gravitational collapse » event?
This would show them three things (which they did were not trying to find out, or maybe):
1. I think these questions are stupid.
2. I know that clear requirements and edge-cases are important
3. I’m an asshole and possibly not fun at parties
I got this vibe at AWS, interviewing in 2020. They asked me to design a stock price tracking webapp. I started asking questions and sketching things out and at each question (fairly basic ones, too, like, how many users are we supporting, how frequently do they request updates, and how timely does the data need to be). Seemed reasonable to me but I think my line of questions annoyed them because they said, "just design the app!" Maybe they thought I was stalling? Hmm, ok, but it'll fall over on day 2. I turned down the offer.
This is starting to sound like the old joke about a coconut laden swallow from (the film) The Holy Grail. I would pay to see the interviewer sweat as you ask the follow-up questions! You sound like fun at a party!
The intake rate of a microscopic black hole is too small to measurably absorb much matter before it falls through to the bottom of the lake until it reaches the center of the planet and oscillates there.
The more pressing thing is that every thing around the lake is irradiated by the evaporation of the microscopic black hole, which supposedly emits quite a lot of energy, as it falls through the bottom.
According to wikipedia, microscopic is considered up to 1 micron. [1] According to the Schwartzchild formula [2] r=(2Gm)/(c^2) so if I take the largest black hole the definition would allow, the mass would be about 10% of the moon. You'd feel 1G at about 60km distance because of it. But indeed, it would fall and take about 20 minutes to reach the core of the planet, while displacing a whooping 1gram of matter. Kind of funny how wierd this whole thing is.
You drop a bowling ball off a space boat into a black hole. Has the amount of mass inside the universe increased, decreased, or stayed the same, ignoring the effects of all other changes?
The amount of mass inside the universe has stayed the same, it just moved from the boat into the black hole.
You're really bored at work one day so to entertain yourself you create 1kg of antimatter along with 1kg of matter. Has the mass in the universe increased or stayed the same?
I'm not sure what other effects I should ignore, but the mass would increase. The ball gains relativistic mass as it accelerates towards the black hole.
PS: Assuming the boat isn't falling too (it's still in orbit), dropping the ball does nothing. You need to decelerate it (reduce it's orbital speed) for it to fall into the black hole.
So for the bowling ball, I replace it with an imaginary marble weighing 1 ton and the answer is now self-evident.