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Question:

A disk and a sphere of the same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

Both reach at the same time

Sphere

Depends on their masses

Disk

Solution:

a = g sinθ * (1 + k²/R²)
For disc: k²/R² = 1/2 = 0.5
For sphere: k²/R² = 2/5 = 0.4
Since, a(sphere) > a(disc) => Sphere will reach first