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?

NCERT Class IX
Sciences - Main Course Book

Chapter 10. Gravitation

Answer 1

In reality, there is a lot of air on top of the cotton bag.  The atmospheric pressure is 1 atm = 10⁵ Newtons / m².

If the surface area of the cotton bag is 4 meter square, then the weight of air column on top of the cotton bag = 10⁵ * 4 = 400, 000 kg.

If the platform of the weighting machine and iron bar is  3 m², then the weight due to air column on weighing machine, when the iron bar is placed = 3 * 10^5 kg.

Thus the reading is more when the cotton bag is placed on the weighing machine.

Answer 2

We know that,

Measured weight of the body = Actual weight of the body - Buoyant force

Therefore,

Actual weight = Measured weight + Buoyant force

As measured weight of cotton and iron is same, actual weight will only depend on the buoyant force.

Buoyant force is given by:

B = Volume of the body × g × Density of air.

Buoyant force is directly proportional to the volume of the body.

As volume of iron is less than the volume of cotton, therefore buoyant force acting on the iron will be less than that of iron.

Hence, actual weight of the cotton will be more than the iron