A vector quantity
c) always zero
65. The balls of iron and aluminium of same diameter are dipped in water. Which is the correct state?
a) The upthrust on the iron ball will be more than the aluminium ball.
b) The upthrust on aluminium ball is more than the iron ball.
c) The upthrust on both balls will be the same.
d) None of the above
Answer (2)
Archimedes' principle states that upthrust equals the weight of displaced fluid.
The balls have the same diameter, thus displacing equal volumes of water.
Equal volumes of displaced water mean equal upthrust forces.
Therefore, the upthrust on both balls is the same: The upthrust on both balls will be the same.
Explanation
Problem Analysis We have two balls, one made of iron and the other of aluminum, both with the same diameter. They are both submerged in water, and we need to determine which statement about the upthrust on the balls is correct.
Applying Archimedes' Principle The upthrust on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. This is known as Archimedes' principle. Since both balls have the same diameter, they have the same volume. When the balls are dipped in water, they displace the same volume of water. Therefore, the upthrust on both balls will be the same, regardless of the material they are made of (iron or aluminum).
Conclusion Based on Archimedes' principle, the upthrust depends only on the volume of water displaced, which is the same for both balls since they have the same diameter. Therefore, the upthrust on both the iron and aluminum balls will be the same.
Examples
Imagine you have two identical toy boats, one made of plastic and the other of wood. If you place both in water, they will displace the same amount of water, and the upward force (upthrust) acting on them will be the same, allowing them to float at the same level. This principle is crucial in designing ships and submarines, ensuring they can float or submerge as intended.
The upthrust on both the iron and aluminum balls will be the same because they displace equal volumes of water due to having the same diameter. This is explained by Archimedes' principle, which states that the buoyant force equals the weight of the displaced fluid. Hence, the correct option is c) .
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