Question

How is the weight of water displaced by a floating body related to the weight of the body itself?
A) Weight of the water displaced by the floating body is greater than weight of the body.
B) Weight of the water displaced by the floating body is less than the weight of the body.
C) Weight of the water displaced by the floating body is equal to weight of the body.
D) Cannot be determined.

Answer 1

Hint: This question has a direct answer based on the law of flotation, which is based on the Archimedes principle, which states that when a body is immersed partly or wholly in a liquid, there is an apparent loss in the weight of the body which is equal to the weight of liquid displaced by the body.

Complete answer:
Let us examine the Archimedes principle again –
When a body is immersed partly or wholly in a liquid, there is an apparent loss in the weight of the body which is equal to the weight of liquid displaced by the body.
Consider a body floating in water as shown:

Archimedes' principle allows the buoyancy of any floating object partially or fully immersed in a fluid to be calculated easily. The downward force on the object is the weight W.
The force acting on the upward, ${F_A}$ is called the buoyant force. This force is responsible for keeping the body in balance position inside the liquid.
For equilibrium,
${F_A} = W$
So, where does this buoyant force arise from?
This buoyant force is nothing, but equal to the weight of water displaced by the body.
Thus, we see here, that the weight of the displaced water is equal to the weight of the body.

Hence, the correct option is Option C.

Note: When it is mentioned that the body is immersed in water, the students should take heed as to whether it is fully or partially immersed, when using the same in calculations. When a body is partially immersed, the weight of the displaced liquid will be equal to that of the immersed portion of the body, and not the whole weight of the body.