Question

You have a bag of cotton and an iron bar, each indicating a mass of $100\mathrm{kg}$ 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

• The cotton bag has a larger volume than an iron bar. So it displaces more air, and so the buoyant force exerted on the cotton bag as a result of the air is greater than that acting on the iron bar (in accordance with Archimedes' principle).
• $\mathrm{True}\mathrm{weight}=\mathrm{Apparent}\mathrm{weight}+\mathrm{Buoyant}\mathrm{force}$
• Since both have an apparent weight of $100\mathrm{kg}$, however, their buoyant forces are different.

Therefore cotton bag is heavier than an iron bar

• $\mathrm{True}\mathrm{weight}\mathrm{of}\mathrm{cotton}>\mathrm{true}\mathrm{weight}\mathrm{of}\mathrm{iron}$