Question

A football has less inertia than a stone of the same size because:
A. Football has more air inside than the stone
B. Football has less air inside than the stone
C. Football has less mass than the stone
D. Football has more mass than the stone

Answer 1

Hint:In order to compare the inertia of the football and stone, we must consider the factors affecting the inertia of a body, that is, to which factors is the inertia directly proportional and to which factors the inertia is inversely proportional. One of the most important properties of an object deciding its inertia is the mass of the body.

Complete solution:
The inertia of a body is expressed as $I=m{{K}^{2}}$
Where,
$m=$mass of body
$K=$radius of gyration of body

It is clearly visible that the inertia of a body is directly proportional to its mass.
Same size of the stone and the football implies that both of them have equal volume but their density and hence, masses are different. Football has air filled in it which is less dense than the stone.

Therefore, the mass of stone is greater than the mass of football because the mass of air acquiring the same space (or volume) is much less than the mass of stone.

Therefore, the correct option is (C) Football has less mass than the stone.

Note:
Technically, inertia is the property of a body, by virtue of which the body opposes or resists a change in its current state of motion by any external force acting on it. This means the inertia of a body at rest will try to resist all factors to continue being at rest and the inertia of a body in motion tries to resist all factors to continue being in the state of motion (it will also resist the body from getting accelerated during motion).