Density problem for physics?

Question

So there are two identical cups filled to the same level with a liquid. Glass 1 has a cube with a density of 619 floating with half of its volume submerged, Glass 2 has a cube with a density of 1435 which is completely submerged to the bottom of the cup. Both blocks have the same volume of .03. What's the density of the liquid?

Please help! Thanks!

Answer 1

Let us consider the 1st cup ;

Volume of the block submerged = 0.03/2 = 0.015

Density = 619

Now use the Archimedes' Principle

Buoyant force = Weight of liquid displaced

Also since the block is in equilibrium, its weight is balanced by the buoyant force.

0.03 * 619 * g = 0.015 * d * g     (d is the density of the liquid)

So d = 1238

Glass 2 has a cube with a density of 1435 which is "completely submerged to the bottom of the cup". This means that the block sinks in the liquid. So its density lust be greater than the density of the liquid.

i.e.

1435 > d

which supports our answer, d = 1238

Hope this helps.

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