Question

A football and a stone have the same mass

• A. both have the same inertia
• B. both have the same momentum
• C. both have different inertia
• D. both have different momentum

Answer 1

The correct option is A

both have the same inertia

Step1: Given data

The mass of a football and a stone is the same

Step2: Formula used

1. Momentum is the quantity of motion of a moving body as measured by the product of its mass and velocity.
2. The product of mass and radius equals the moment of inertia. $I=m{r}^2$

Step3: Analyzing the situation.

1. 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.
2. The sum of the products of the mass of each particle in the body with the distance squared from the axis of rotation is known as the moment of inertia of a solid sphere.
3. As a solid spherical, football and stone are utilized. Football's moment of inertia must be computed. Using the solid sphere moment of inertia formula $I=\frac{2}{3}M{R}^2$
4. Putting the value into the formula $I=m{r}^2$
5. The moment of inertia must be the same if the mass of a football and a stone are the same.
6. The momentum would be identical if the football and the stone had the same velocity, however, neither the football nor the stone's velocity is given.
7. As a result, both have the same inertia.

Hence, option A is the correct answer.