Exploring Motion on an Inclined Plane

What is the order in which the disk, hoop, and solid sphere reach the bottom of the inclined plane?

a. Disk, hoop, sphere
b. Hoop, sphere, disk
c. Sphere, disk, hoop
d. Sphere, hoop, disk
e. Hoop, disk, sphere

Answer:

The correct order in which the objects reach the bottom of the inclined plane is: d. Sphere, hoop, disk

When objects roll without slipping, their motion is determined by their rotational inertia, which depends on their mass distribution. The objects' rotational inertia is related to their shape and mass distribution. In this scenario, the solid sphere has the highest rotational inertia among the three objects.

Due to its higher rotational inertia, the sphere takes more time to rotate and roll down the inclined plane, causing it to reach the bottom first. The hoop, with a lower rotational inertia compared to the sphere but higher than the disk, follows next in reaching the bottom.

Finally, the disk has the lowest rotational inertia among the three objects, primarily due to its mass distribution. As a result, the disk reaches the bottom last, following the sphere and the hoop. Therefore, the correct order of reaching the bottom of the inclined plane is sphere, hoop, and then disk.