Question

Given a block of iron of height 5.00 cm of density 7.85 grams/cm^3. It sinks in water. Which of these changes could be made to the iron to make it float in a fluid? A)cut it in half B)cut a quarter of it off C)cut 75% of it off D)put it in liquid mercury of density 13.5 grams/cm^3 E)put it in water combined with another fluid that increases its density to 1.8 grams/cm^3

Answer 1

We are given a block with a density of 7.85 g/cm^3. We are asked to make changes to it so that it can float in water.

An object floats in water if its density is greater than that of water, therefore an object floats if:

`\rho_(object)<\rho_(water)`

Therefore, we need to make a change that will change the density of the system.

Since density is a property of the material of the object and not of its dimensions, cutting the object will not change its density and therefore it will still sink.

If we put the object in water combined with a fluid with a density of 1.8 g/cm^3, then we would have:

`1.8<7.85`

This means that the object would have a density that is greater than the density of the fluid and therefore, it will sink.

If the object is put in a liquid with a density of 13.5 g/cm^3, then we would have:

`13.5>7.85`

Since the density of the object is less than the density of the liquid this means that the object will float, therefore, the right answer is D.