Anyone who is good at math and physics, please answer this!?

Question

Neopia is a strange little planet. Its gravitational acceleration at its surface is exactly 10.0 metres per second per second, and its diameter is exactly 2100 kilometres.

Also, a completely unrelated fact, Skeiths are able to consume about 0.4 kg of pretty much anything they want to eat, every minute, nonstop.

Assuming that the density of the planet is uniform, and that orbiting bodies don't significantly affect the planet's gravity, how many years will it take one million Skeiths to consume one cubic kilometre of Neopia? Please round up to the nearest year.

Answer 1

74 minutes, I think?

Answer 2

Let the density of Neopia be ρ kg/m^3.

g = GM/r^2 = G(4/3 π r^3 ρ) / r^2 = G (4/3 π r ρ)
So ρ = 10.0 / [(6.67×10^-11) (4/3)(π) (1.05×10^6)] = 3.41×10^4 kg/m^3.

So the mass of 1 cubic kilometre of Neopia will be (1000)^3 (3.41×10^4) = 3.41×10^13 kg.

One million Skeiths will consume 4×10^5 kg per minute, so the number of minutes required is 3.41×10^13 / 4×10^5 = 8.52×10^7. This works out to 1.42×10^6 hours, or 5.92×10^4 days, or 162 years to the nearest year.

Answer 3

I made millioins in the neopia stock market.