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A uniform hoop, disk, and sphere, with t...

A uniform hoop, disk, and sphere, with the same mass M and same radius R, are released simultaneously from rest at the top of a ramp of length L = 2.5 m and angle `theta = 12^(@)` with the horizontal. The objects roll smoothly down the ramp.
(a) Which object wins the race to the bottom of the ramp?

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AI Generated Solution

To determine which object (hoop, disk, or sphere) wins the race to the bottom of the ramp, we need to analyze the motion of each object as they roll down the ramp. ### Step-by-Step Solution: 1. **Identify the Objects and Their Properties**: - We have three objects: a uniform hoop, a disk, and a solid sphere. - All objects have the same mass \( M \) and the same radius \( R \). ...
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