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 lead and glass samples have the same volume (1.0 cm³), so they displace the same amount of water, which is 1.0 cm³, when submerged in the beakers. This is based on the concept of water displacement, which states that the displaced water's volume equals the submerged object's volume.

Step-by-step solution

Identify the given volume of the samples

The two samples, lead and glass, each have the same volume, which is 1.0 cm³.

Understand the concept of water displacement and Archimedes' principle

When an object is submerged in a liquid, the liquid level is pushed up, and the volume of liquid displaced is equal to the submerged object's volume. This concept is called water displacement. According to Archimedes' principle, the buoyant force (which pushes the object up) exerted on a submerged object is equal to the weight of the fluid displaced by the object.

Determining the volume of water displaced by the lead sample

When the lead sample is submerged in water, it displaces the water equal to its volume. Since the volume of the lead sample is 1.0 cm³, it displaces 1.0 cm³ of water.

Determining the volume of water displaced by the glass sample

When the glass sample is submerged in water, it displaces the water equal to its volume. Since the glass sample's volume is 1.0 cm³, it displaces 1.0 cm³ of water.

Comparing the volumes of water displaced by the samples

Both the lead and glass samples have the same volume (1.0 cm³), and thus, both samples displace the same volume of water when submerged in the beakers, which is 1.0 cm³.