Question

100kg of iron and cotton are weighed by using a spring balance on surface of earth. If R1 and R2 are the readings shown by balance thwn R1 >R2. Why?

Answer 1

If we assume the true mass of both iron and cotton to be 100 kg, and then measure their weight on a weighing machine, iron will be heavier. This can be explained by the concept of buoyant force in fluid statics:

Apparent weight = mg - upthrust , where m is the true mass of the object and g is acceleration due to gravity.

( Note here that a weighing machine measure the apparent weight of an object.)

Now, density of cotton is less than that of iron. So, 100 kg of cotton will occupy more space than 1 kg iron, and hence displace more volume of air. And since upthrust is directly proportional to volume of fluid displaced, cotton will experience more upthrust than iron.

Thus, the apparent weight of 100 kg iron will be more than that of 100 kg cotton, and hence it will feel heavier.

PS : All this is true if we consider the surrounding to be earth's atmosphere. If the surrounding is vacuum (for example, outer space), then both will have the same apparent weight (as upthrust is zero), and hence will feel equally heavy.