A disc and a sphere of 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?

Acceleration of a rolling body is \( a = \frac{g\sin\theta}{1 + I/MR^2} \). For a sphere, \( I/MR^2 = 2/5 \), so \( a = \frac{5}{7}g\sin\theta \). For a disc, \( I/MR^2 = 1/2 \), so \( a = \frac{2}{3}g\sin\theta \). Since acceleration of the sphere is greater (\( 5/7 > 2/3 \)), the sphere reaches the bottom first.