Use Archimedes’ principle to prove the following: “When a body is floating on a liquid, it displaces a weight of liquid equal to its own weight.”
The correct answer and explanation is:
Correct Answer:
Archimedes’ principle states that a body partially or wholly immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by it. Using this principle, the floating condition can be proven as follows:
When a body is floating on a liquid, it is in equilibrium. This means the upward buoyant force exerted by the liquid balances the downward weight of the body. According to Archimedes’ principle, this upward buoyant force is equal to the weight of the liquid displaced by the submerged part of the body. Therefore, for a floating object:
Weight of the body = Weight of the displaced liquid
This proves the statement.
Explanation (300 words):
Archimedes’ principle is a fundamental law in fluid mechanics. It provides a clear explanation of buoyancy, the force that allows objects to float. When a body is placed in a fluid such as water, it pushes aside or displaces some of the fluid. In return, the fluid exerts an upward force known as the buoyant force.
This buoyant force is exactly equal to the weight of the fluid that has been displaced. Now, if the body is completely submerged but sinks, the weight of the body is greater than the buoyant force. If the body floats, it means there is balance: the weight of the body is equal to the buoyant force.
A floating body is only partially submerged. The portion that is under the fluid displaces a certain volume of liquid. This displaced volume has a specific weight. Since the body is floating without rising or sinking, it must be in equilibrium. That means the downward force due to gravity acting on the body is exactly equal to the upward buoyant force acting on it.
As Archimedes’ principle tells us, the buoyant force equals the weight of the displaced fluid. Thus, the only way for a body to float and remain at rest is if the weight of the body is equal to the weight of the displaced liquid. This condition must always be satisfied for any floating object, whether it is a boat, a log, or a plastic container.
Hence, when a body is floating on a liquid, it displaces a weight of liquid equal to its own weight.