Question

A rock sits at the bottom of a fish tank and the level of the water in the tank is noted. The rock is then put into an old fashioned ice cube tray (made from aluminium) and is floated on the top of the water. The level is again noted. Which of the following is true?

a). The water level is the same before and after.

b). The water level is higher before when rock is at the bottom of the fish tank.

c). The water level is higher after when the rock is floating in the tray.

d). The rock cannot float in a metal ice cube tray.

e). Cannot determine without more information.

Answer 1

Answer : (c) The water level is higher after when the rock is floating in the tray.

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This diagram is my attempt to show the situation first when the rock is in the boat and secondly when you've chucked the rock over the side.

This diagram is my attempt to show the situation first when the rock is in the boat and secondly when you've chucked the rock over the side.

The mass of the boat of M and the mass of the rock is m. The density of water is ρ_water and the density of the rock is ρ_rock.

In the first case Archimedes' principle tells us that the volume of water displaced is:

In the second case the volume of water displaced is:

where the second term is just the volume of the rock. If we take the difference of these two we get:

I think it's safe to assume that ρ_rock > ρ_water, i.e. the rock sinks in water, and in that case V_disp,1 − V_disp,2 is positive i.e. more water is displaced when the rock is in the boat.

Therefore, The water level is higher after when the rock is floating in the tray.