Question

A small uniform disk and a small uniform sphere are released simultaneously at the top of a high inclined plane, and they roll down without slipping. Which one will reach the bottom first?A) the one of smallest diameter B) the one of greatest mass C) the disk D) the sphere E) They will reach the bottom at the same time.

Answer 1

Answer:

(D) the sphere

Explanation:

The bodies given are Disk and Solid sphere (uniform sphere)

Moment of inertia of the bodies are

I(disk) = $\frac{MR^2}{2}$

I(sphere) = $\frac{2MR^2}{5}$

Since the moment of inertia of sphere is less than that of disk, therefore sphere will reach the bottom first.