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.
