Chapter 8, Problem 19Q

To determine

To Describe: The experiment to find which is hollow and solid.

Explanation of Solution

Given information:

Two Spheres look identical and have the same mass. However, one is hollow and the other is solid.

Formula used:

The torque is $\tau =I\alpha =\text{constant}$

Here,

  $I$ is the moment of inertia,

  $\alpha$ is the angular acceleration.

Calculation:

Two spheres look identical. One is hollow and the other is solid. Spin each on the table. The sphere which spins at a lower rate will be the hollow sphere. This is because in a hollow sphere, the air inside tries to get away from the axis of rotation. Therefore, its moment of inertia $I$ increases.

As the torque $\tau =I\alpha =\text{constant}$ , $\alpha$ decreases, therefore the hollow sphere will spin with smaller angular acceleration.

In the case of a solid sphere, it will rotate more or less like a rigid body

Conclusion:

A solid sphere will rotate more or less like a rigid body.