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Chapter 3: Problem 112

Three steel balls (each about half an inch in diameter ) lie at the bottom of a plastic shell floating on the water surface in a partially filled bucket. Someone removes the steel balls from the shell and carefully lets them fall to the bottom of the bucket, leaving the plastic shell to float empty. What happens to the water level in the bucket? Does it rise, go down, or remain unchanged? Explain.

Short Answer

Expert verified
The water level in the bucket goes down.

Step by step solution

01

Understand The Initial Setup

Initially, the three steel balls are within a floating plastic shell. Since the shell is floating, we know that according to Archimedes鈥� principle, the weight of the water displaced by the shell and the balls combined is equal to the total weight of the shell and the balls.
02

Observe The Change

When the steel balls are removed from the shell and let go to the bottom of the bucket, there is a change in the amount of water displaced. Now, the weight of the water displaced is equal to the total weight of the empty shell and the three balls separately.
03

Compare The Volume Of The Displaced Water

Since the volume of the steel balls is constant, we know that the balls will displace the same volume of water regardless of whether they are in the shell or at the bottom of the bucket. But, since the steel balls are denser than the shell, when the balls are in the shell, they displace water equal to their own volume plus the volume of the shell. When the balls are on the bottom of the bucket, they displace water equal to their own volume only, because the shell is now empty and displaces less water than before.
04

Conclude On The Water Level

Given the above, we observe that once the balls are moved to the bottom on the bucket, the total volume of water displaced decreases because the shell now being empty displaces less water. This leads to a decrease in the water level.

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Most popular questions from this chapter

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