Two uniform solid balls, one of radius R and mass M, the other of radius 2R and mass 8M, roll down a high incline. They start together from rest at the top of the incline. Which one will reach the
Bottom of the incline first?
A) The large sphere arrives first.
B) The small sphere arrives first.
C) Both reach the bottom at the same time.

Question

Quizplus · Accepted Answer

Both spheres will reach the bottom at the same time because the acceleration of a rolling object down an incline does not depend on its mass or size but only on the gravitational acceleration and the incline angle. Since both spheres are solid and uniform, they have the same distribution of mass relative to their axes of rotation, leading to the same moment of inertia factor in the equation of motion. Therefore, their accelerations are identical, and they reach the bottom simultaneously.

Two Uniform Solid Balls, One of Radius R and Mass