Question.
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 ?
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 ?
Solution:
A weighing machine measures the apparent weight of an object. We know that apparent weight
$\left(\mathrm{W}_{2}\right)$ is equal to true weight $\left(\mathrm{W}_{2}\right)$ minus buoyant force $\left(\mathrm{F}_{\mathrm{B}}\right)$ i.e.,
$\mathrm{W}_{\mathrm{a}}=\mathrm{W}_{\mathrm{i}}-\mathrm{F}_{\mathrm{B}}$
or $\mathrm{W}_{\mathrm{t}}=\mathrm{W}_{\mathrm{a}}+\mathrm{F}_{\mathrm{B}}$
Now, buoyant force on the cotton due to the air present around it is large as compared to the buoyant force on the iron. This is because the volume of cotton is very large as compared to the volume of iron. As a result, the true weight of cotton must be greater than the true weight of iron. Thus, the given cotton sample is heavier than the given iron sample.
A weighing machine measures the apparent weight of an object. We know that apparent weight
$\left(\mathrm{W}_{2}\right)$ is equal to true weight $\left(\mathrm{W}_{2}\right)$ minus buoyant force $\left(\mathrm{F}_{\mathrm{B}}\right)$ i.e.,
$\mathrm{W}_{\mathrm{a}}=\mathrm{W}_{\mathrm{i}}-\mathrm{F}_{\mathrm{B}}$
or $\mathrm{W}_{\mathrm{t}}=\mathrm{W}_{\mathrm{a}}+\mathrm{F}_{\mathrm{B}}$
Now, buoyant force on the cotton due to the air present around it is large as compared to the buoyant force on the iron. This is because the volume of cotton is very large as compared to the volume of iron. As a result, the true weight of cotton must be greater than the true weight of iron. Thus, the given cotton sample is heavier than the given iron sample.