Question

A football and a stone has same mass:
A. Both have same inertia
B. Both have same momentum
C. Both have different inertia
D. Both have different momentum

Answer 1

Hint:Here we will first see the definition of moment of inertia and momentum and then we will see which condition is satisfied among the four given options and then answer the question.

Complete step by step answer:
As given, the mass of a football and a stone is the same.Assume the ball is a football and the stone are solid spheres. The sphere's radius is $r$. We know that the moment of inertia of a solid sphere is known as the sum of the products of the mass of each particle in the body with the distance squared from the axis of rotation.

The quantity of motion of a moving body measured by a product of its mass and velocity is known as momentum. The product of mass and radius equals the moment of inertia.In terms of mathematics,
\[I=M{{R}^{2}}\]
Football and stone are used as a solid sphere here. The moment of inertia of football must be calculated. Using the solid sphere moment of inertia formula
\[I=\dfrac{2}{3}M{{R}^{2}}\]
Putting the value into the formula
\[I=m{{r}^{2}}\]
If the mass of a football and a stone are the same, the moment of inertia has to be the same.As a result, both have the same inertia.

Hence option A is the correct answer.

Note:Here if the football and the stone had the same velocity then the momentum would also be equal but there is nothing mentioned about the velocity of the football or the stone.Inertia is defined as a property of matter by which it remains at the state of rest or in uniform motion in the same straight line unless acted upon by some external force.