A disc, a hoop, and a sphere of the same mass and radius are rolled down from a frictionless, inclined plane. Which has a greater speed on reaching the ground?
Correct answer: C. Sphere
- A. Disc
- B. Loop
- C. Sphere
- D. All have the same speed
Explanation
The sphere has most of its mass near the axis of rotation, so it will have the smallest moment of inertia and will reach the ground first.The disc has its mass uniformly distributed, so will have a greater moment of inertia and will arrive second.The hoop has all its mass concentrated away from the center, so will have the greatest moment of inertia. It will arrive last, but will then travel farther away on the horizontal plane than the other shapes, as it will have stored more of the original potential energy in the form of rotational energy.
This question appeared on the NUMS 2015 paper, which you can sit online with every answer explained.
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