Question

A body of mass 2 kg is floating in the liquid of density 900 kg$m^{-3}$. The weight of the liquid displaced by it is
A. 20 dyne
B. 20 N
C. 2 N
D. None of the above

Answer 1

Hint: A body floats on a liquid because the liquid exerts an upthrust on the body which overcomes its downward acting force (or weight). The weight of the liquid displaced by the body has to be more than or equal to the weight of the body, in order for the body to float.

Complete step-by-step solution:
We are given that the mass of the body is 2 kg. The weight of the body will therefore be:
W = mg
$W = 2 \times 10 N$
When this body is placed on the liquid and we are given that the body floats, this means that the weight of the liquid displaced by the body will be equal to or more than the body's weight.
In the condition when the weight of the liquid displaced by the body is equal to the weight of the body, the force that the body exerts downward on the liquid due to its weight is equal to the force that the liquid is exerting on the body upwards. Therefore, the weight of the liquid displaced by the body is 20 N so the correct answer is an option (B).

Additional information:
1. The overall density also decides whether the body will float or will sink in a liquid. If a body is denser than the liquid, it certainly will sink just like if two liquids are mixed, then the heavier one always settles down (honey and water).
2. Ships made of iron, which is denser than water are able to float because they are able to displace more water.
3. A floating body will remain in equilibrium when the weight of the liquid displaced is equal to the weight of the body and also the center of gravity of the body and center of upthrust lie on the same vertical line.

Note: In the question we are given the mass of the body and we are asked about the weight. One might confuse one quantity for the other and choose the wrong answer. The unit of mass is kg. When we say that a person weighs 50 kg, we must actually consider it to be 50 N. If we consider the acceleration due to gravity to be 10 m/$s^2$, the person weighing 50 kg might have a mass of 5 kg. Mass is not measurable therefore we measure the weight by a weighing machine. Weight is the amount of force that a certain mass exerts downwards due to gravity.