Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A ring, a disc and a solid sphere, all of different masses and sizes, roll from rest without slipping down a ramp high. A block slides down the same ramp with no friction. Taking , find the speed of each at the bottom.
Rolling without slipping: . Kinetic energy: . Down a slope: and ; static friction does no work.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Energy: some goes into turning, the rest into moving along.
Step 1. Block. .
Step 2. Sphere. .
Step 3. Disc. .
Step 4. Ring. .
Answer: Block , sphere , disc , ring .
Check. The order matches the race: the less energy spent on turning, the faster.
Watch out. Masses and radii cancel. Only the shape matters.
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