A solid sphere, spherical shell, solid cylinder and a cylindrical shell all have the same mass m and radius R. If they are all released from rest at the same elevation and roll without slipping, which reaches the bottom of an inclined plane first?

Solid Sphere

Explanation:

The object with the smallest moment of inertia will reach the bottom first.

Moment of inertia of the following:

Solid Sphere = 2/5 mr^2

Spherical Shell = 2/3 mr^2

Solid Cylinder = 1/2 mr^2

Cylindrical shell = mr^2

Since we know all the masses and radii are the same we can replace them with a placeholder value of mr^2 = 1 kgm^2 as an example.

Moment of inertia of the following (our example system):

Solid Sphere = 2/5 kgm^2

Spherical Shell = 2/3 kgm^2

Solid Cylinder = 1/2 kgm^2

Cylindrical shell = 1 kgm^2

We can see that the solid sphere will have the smallest moment of inertia therefore it will reach the bottom first.

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