Chapter 8, Problem 13Q

Two spheres look identical and have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine which is which.

To determine

The solid and the hollow sphere from two spheres having identical looks and the same mass through an experiment.

Answer to Problem 13Q

Solution:

If we rotate the two given spheres with the same force, the hollow sphere will rotate slower than the identical solid sphere. This can easily help us identify the nature of the two spheres.

Explanation of Solution

The moment of inertia of a hollow sphere is given by $I=\left(2/3\right)m{r}^2$ , while that of a solid sphere is given by $I=\left(2/5\right)m{r}^2$ . Therefore, for the same mass and radius, a hollow sphere has greater moment of inertia.

By the relation $\text{τ = I}\times \text{α}$ , for the same torque applied on two identical bodies, the one with the greater I will have lower angular acceleration ( a ).