Question

A hoop, a solid cylinder, a solid sphere, and a thin, spherical shell each have the same mass of 4.70 kg and the same radius of 0.233 m.

(b) Each object is rolled down the same ramp, each starting from rest at the same initial height. Each rolls without slipping. Rank the translational speed at the bottom of the ramp for each object from highest to lowest.

A. solid cylinder > thin spherical shell > solid sphere > hoop

B. solid sphere > solid cylinder > thin spherical shell > hoop

C. hoop > solid cylinder > solid sphere > thin spherical shell

D. thin spherical shell > solid sphere > solid cylinder > hoop

Answer 1

The translational speed at the bottom of the ramp for each object is ranked from highest to lowest is option A)) solid cylinder > thin spherical shell > solid sphere > hoop.

Step-by-step explanation:

To rank the translational speed at the bottom of the ramp for each object, we need to consider their moments of inertia.

The moment of inertia of each object is determined by its shape and mass distribution. In this case, since each object has the same mass and radius, the moment of inertia can be compared based on their shapes.

The moment of inertia for each object from highest to lowest is: hoop, solid cylinder, solid sphere, thin spherical shell.

This means that the translational speed at the bottom of the ramp will be highest for the hoop, followed by the solid cylinder, solid sphere, and the thin spherical shell.

Therefore, the correct ranking for the translational speed at the bottom of the ramp for each object is: Option A. solid cylinder > thin spherical shell > solid sphere > hoop.