A solid cylinder,a hollow cylinder,and a square block of equal masses are released at the top of an inclined plane.The cylinders roll down and the block slides down,all with negligible frictional losses.Which of the following will happen?
A)The hollow cylinder arrives at the bottom first.
B)The solid cylinder arrives at the bottom first.
C)The block arrives at the bottom first.
D)They all arrive at the bottom simultaneously.
E)None of these will happen.

Question

Quizplus · Accepted Answer

For each object, its potential energy at the top is converted to kinetic energy at the bottom. The potential energy is given as mgh, where m is the mass, g is the acceleration due to gravity, and h is the height of the incline. As they all have equal mass and are released at the same height, their potential energy is the same. At the bottom, their kinetic energy will be different depending on their motion. 
The hollow cylinder will roll down without slipping, meaning its energy will be a combination of rotational and translational kinetic energy. The solid cylinder will also roll down without slipping, but due to its mass distribution, it will have more rotational kinetic energy than the hollow cylinder. The block will slide down and have only translational kinetic energy. The amount of rotational kinetic energy an object has will not affect its speed, as it is applied to the rotation of the object and not its movement down the incline. Therefore, the block, having only translational kinetic energy, will have the highest speed and arrive at the bottom first.

A Solid Cylinder,a Hollow Cylinder,and a Square Block of Equal