A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is where .

Question

A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is  where  .

Canvas Classes · Accepted Answer

🧠  — Take the Ratio Directly

Both bodies start from rest, roll without slipping down the same incline (same height ). The velocity at the bottom depends only on :

For a ring (about its centre-perpendicular axis): .

For a solid sphere (about its diameter): .

🗺️ Working It Out

Ratio:

Matching the form : , giving . The stored answer key gives  — please cross-check against the official source.

⚡ The Smart Move

For "two rolling bodies, same height" problems,  depends only on . Big

More questions from this chapter

More questions from this chapter