Question

Which of the following has a higher inertia: a football or a stone of the same size?

Answer 1

We need to find which one of football and stone has higher inertia even if they are of the same size. So, we need to check on what factors do the inertia depend on. The most important factor on which inertia depends is the mass and the radius of the body.

Complete answer:
Inertia is the property of an object by which the object remains at rest or in uniform motion in the same straight line unless it is acted upon by some external force.
Inertia of body is given by: $I=m{{K}^{2}}$
Where, I = inertia of the given body.
m is the mass of the given body.
K is the radius of gyration of the given body.
So, we can clearly see that the inertia of the given body depends on its mass and its radius. inertia is directly proportional to the mass of the given body and directly proportional to the square of the radius of the given body.
Here in this question, it is given that the football and the stone have the same size which implies that both of them will have the same radius, so the inertia will not be changed because of the radius. So now, we have to take the account of mass of the given bodies.
We know that football is filled with air so it will be less dense than stone and hence will have less mass as compared to the stone. And we know this too that inertia is directly proportional to mass of the body . The more the mass the more is the inertia and the less the mass the less the inertia. And here, we know that the mass of stone is higher than that of football.
So, stone will have higher inertia than football even if both of them have the same size.

Note:
This also gives us the account of first law of motion given by the scientist Isaac Newton that is if a body is in motion it tends to remain in motion and if a body is rest it tends to remain in rest unless any external force is applied on it, because it also depends on inertia only.