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

When both the bag of cotton and the iron bar register a mass of 100 kg on a weighing machine, it might seem puzzling as to which one is actually heavier. The weighing machine indicates their weights as equal, but in reality, the iron bar is heavier than the bag of cotton. Here’s an informative breakdown:

1. Measurement on the Weighing Machine: The weighing machine measures the force exerted by the objects due to gravity, which is their weight. In this case, both the cotton bag and the iron bar register as 100 kg on the machine.

2. Understanding Density: Density is the amount of mass packed into a specific volume. Iron has a significantly higher density than cotton. Even though both show the same mass on the weighing machine, the density of the materials is vastly different.

3. Volume Discrepancy: Despite the same indicated mass on the weighing machine, the volume of a 100 kg iron bar is much smaller than that of a 100 kg bag of cotton because iron is much denser than cotton.

4. Comparing Actual Mass: If we were to directly measure their volumes, we’d find that the iron bar has a much smaller volume compared to the bag of cotton due to the density difference. However, their indicated mass on the machine remains the same.

5. Conclusion: Due to the substantial difference in density, the iron bar is significantly heavier than the bag of cotton, even though the weighing machine shows them having the same mass. This discrepancy arises from the iron’s higher density, allowing it to contain a much larger mass within a smaller volume compared to cotton.

Therefore, while the weighing machine registers their masses as equal, the iron bar is indeed heavier than the bag of cotton due to its higher density, resulting in a larger actual mass within a smaller volume.