Question

three objects are at the top of an inclined plane: a disk, a sphere, and a ring. all of the objects have the same radius and the same mass. which object would finish last in a race down the incline if they are all released from rest? (hint: use conservation of energy methods, and note that at the bottom there is both translational and rotational energy)

Answer 1

The ring would finish at last in the race down the incline.

Incline is a a plane surface tilted at some angle from the horizontal.

The moment of inertia of the ring = $mr^{2}$

The moment of inertia of the disc = ( $mr^{2}$ ) / 2

The moment of inertia of the solid sphere = 2( $mr^{2}$ ) / 5

Since the moment of inertia is the resistance to rotational motion, we see that the object with the smallest moment of inertia will reach the bottom first.

The gain in total kinetic energy is equal to the loss in gravitational potential energy, which in turn is the same for all the objects and is equal to 'mgh'

where h is the height of the inclined plane.

So the order of reaching the bottom is Sphere, disc and ring.

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