Question Detail
Question
Starting from rest, a solid cylinder and a hollow sphere (with a thin wall) of the same mass and radius roll without slipping down the same inclined plane. Which statement about their speeds at the bottom is correct?
Correct Answer
Option B is the correct answer.
Detailed Explanation
The object with the smaller moment of inertia relative to its mass and radius will have a larger fraction of its total kinetic energy as translational energy, and thus a greater linear speed at the bottom. For a solid cylinder, I/MR² = 1/2; for a hollow thin-walled sphere, I/MR² = 2/3. Since 1/2 < 2/3, the solid cylinder has a smaller rotational inertia fraction and will reach a higher speed.
Hint
Compare the moments of inertia of the two objects. Which one has a larger proportion of its mass farther from the axis of rotation?