How Long Does It Take for a 1kg Black Hole to Absorb 10kg of Mass?

[hydrostar905]

Homework Statement

A crazy scientist creates a black hole with a mass of 1 kilogram. The black hole gets lost, as it shifts to the center then oscillates. Assume that the Earth is all water with the same density and the same temperature of 4 degrees celsius. With the black hole moving at a speed of 30 meters per second constantly, how much time does it take for the black hole to suck in 10 kg of mass?

Homework Equations

Schwartzchild radius
(any others?)

The Attempt at a Solution

I got the schwarzschild radius of 120,060 kilograms. I also found that 1 kilogram is equal to 5.03 x 10^(-31) solar masses. I'm not sure where to go after getting the schwarzschild radius and solar mass, however, plus I'm puzzled about how the "earth being all water" is put into the problem using mathematics. This is an important grade for my college, class, however, so any help is GREATLY appreciated!

Thank you!

 

[anathema]

Thank you for your post. I am always intrigued by questions related to black holes and their behavior. Let's take a closer look at the problem and see if we can find a solution.

First, let's clarify some concepts. The Schwarzschild radius is the radius at which the escape velocity is equal to the speed of light, and is given by the equation Rs = 2GM/c^2, where G is the gravitational constant, M is the mass of the black hole, and c is the speed of light. In this case, with a mass of 1 kilogram, the Schwarzschild radius would be 1.48 x 10^-27 meters.

Now, let's consider the Earth being all water with a density of 1000 kg/m^3. This means that every cubic meter of water has a mass of 1000 kilograms. Since we are looking at a black hole with a mass of 1 kilogram, it would take 0.001 cubic meters of water to equal its mass.

Next, we need to consider the speed of the black hole, which is given as 30 meters per second. This means that the black hole will cover a distance of 30 meters in one second.

Now, we can calculate the time it would take for the black hole to suck in 10 kilograms of mass. We can do this by dividing the mass of 10 kilograms by the mass of 1 kilogram (since the black hole is moving at a constant speed) and then multiplying by the distance of 30 meters. This gives us a total distance of 300 meters.

Using the formula for velocity (v = d/t) we can rearrange it to solve for time (t = d/v). Plugging in the values, we get a time of 10 seconds. This means that it would take 10 seconds for the black hole to suck in 10 kilograms of mass.

I hope this helps to clarify the problem and guide you in the right direction. Please let me know if you have any further questions. Good luck with your studies!