Question

You have a bag of cotton and an iron bar, each indicating a mass of 100kg when measured on a weighing machine. In reality, one is heavier than the other. Can you say which one is heavier and why?

Answer 1

Hint: The apparent weight of the body depends upon the weight of the surrounding fluid displaced by it. Objects having more volume will displace more volume. Objects having less density will occupy more volume compared to objects having more density and having the same mass.

Complete answer:
There are many factors that you need to take into consideration when you weigh something.
According to Archimedes' principle an object immersed in a fluid experiences a buoyant force which is equal to which is equal to the weight of the fluid displaced by it.
Thus,
Apparent weight = True weight – Weight of the displaced fluid ……… (i)

This buoyant force is nothing but the upthrust exerted due to fluid molecules. The direction of this buoyant force is opposite to the direction of gravitational force.
More the volume of an object, more it will displace the fluid, and thus more will be buoyant force acting on it.
Therefore, according to expression (i), if the amount of displaced fluid is more, its apparent weight will be less.
We can modify equation (i) as

True weight = Apparent weight + Weight of the displaced fluid ……… (ii)

In the question, it is given that a bag of cotton and an iron bar indicate a mass of 100kg when measured on a weighing machine. It means they both have the same apparent weight.
If we add this condition in equation (2), then we can conclude that an object displacing more fluid will have more weight in reality i.e. more true weight.
When we measure anything on a weighing machine, air is fluid present around it and that object will displace air depending upon its volume.
Density of an object is the ratio of its mass to volume.

i.e. \[\text{Density=}\dfrac{\text{Mass}}{\text{Volume}}\]

Therefore, density is inversely proportional to the volume. Hence more the mass, less will be its density and vice versa.
We know that cotton has less density compared to iron bars. Therefore, cotton will occupy more volume than an iron bar if both have the same weight.
Thus, as cotton has more volume compared to iron bars, it will displace more air surrounding it and hence, it will have more weight in reality.
Therefore, in reality, cotton is heavier than an iron bar in a given case.

Note:
Since apparent weight depends on the volume of fluid displaced by it, while weighing you should take care that objects in both weighing pans have comparable size. The surrounding temperature, pressure and humidity also affect the apparent weight. The weighing object should not be hot and wet.