Two cylinders made of the same material roll down a plane inclined at an angle θ with the horizontal. Each travels the same distance. The radius of cylinder B is twice the radius of cylinder A. In what order do they reach the bottom?
A) A reaches the bottom first because it has the greater acceleration.
B) A reaches the bottom first because it has a smaller moment of inertia.
C) B reaches the bottom first because is experiences a larger torque.
D) B reaches the bottom first because it travels a larger distance in one rotation.
E) They both reach the bottom at the same time, because each has the same linear acceleration.

Question

Quizplus · Accepted Answer

Both cylinders will reach the bottom at the same time because they both have the same linear acceleration due to gravity, regardless of their radius or moment of inertia. This is because the acceleration is determined by the angle of the incline and the force of gravity acting on the cylinders, which is the same for both. The distance traveled in one rotation may be different for the two cylinders, but this does not affect the time taken to reach the bottom. Similarly, the torque experienced by each cylinder depends on its mass, radius and angle of inclination, and is not directly related to the time taken to reach the bottom. Therefore, the correct answer is E.

Two Cylinders Made of the Same Material Roll Down a Plane