Question

You have a \(1.0-\mathrm{cm}^{3}\) sample of lead and a \(1.0-\mathrm{cm}^{3}\) sample of glass. You drop each in separate beakers of water. How do the volumes of water displaced by each sample compare? Explain.

Short answer

Both the \(1.0-\mathrm{cm}^{3}\) sample of lead and the \(1.0-\mathrm{cm}^{3}\) sample of glass displace the same volume of water (\(1.0-\mathrm{cm}^{3}\)) when submerged, according to Archimedes' principle. This is because the volume of water displaced is only dependent on the volume of the object and not on the object's material.

Step-by-step solution

Recall Archimedes' principle

Archimedes' principle states that the volume of fluid displaced by an object submerged in the fluid is equal to the volume of the object. This means if we submerge a \(1.0-\mathrm{cm}^{3}\) object in water, it will displace exactly \(1.0-\mathrm{cm}^{3}\) of water.

Calculate the volume of water displaced by the lead sample

Since the volume of the lead sample is \(1.0-\mathrm{cm}^{3}\), according to Archimedes' principle, it will displace exactly \(1.0-\mathrm{cm}^{3}\) of water.

Calculate the volume of water displaced by the glass sample

Similarly, since the volume of the glass sample is also \(1.0-\mathrm{cm}^{3}\), according to Archimedes' principle, it will displace exactly \(1.0-\mathrm{cm}^{3}\) of water.

Compare the volumes of water displaced

Now that we know the lead and the glass samples each displace \(1.0-\mathrm{cm}^{3}\) of water, we can conclude that the volumes of water displaced by each sample are equal. Since the volume displaced is only dependent on the volume of the object and not on the object's material, it doesn't matter that the objects are made of different materials.