A disk and a ring of the same mass and radius are rolling down an incline. Which

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Question: A disk and a ring of the same mass and radius are rolling down an incline. Which will reach the bottom first?

Options:

Correct Answer: Disk

Solution:

The disk has a smaller moment of inertia compared to the ring, hence it will reach the bottom first.

A disk and a ring of the same mass and radius are rolling down an incline. Which will reach the bottom first?

A disk and a ring of the same mass and radius are rolling down an incline. Which will reach the bottom first?

Step 1: Understand that both the disk and the ring have the same mass and radius.
Step 2: Learn about moment of inertia, which is a measure of how difficult it is to change the rotation of an object.
Step 3: Know that the disk has a smaller moment of inertia than the ring. This means the disk is easier to roll.
Step 4: Realize that when both objects roll down the incline, the one with the smaller moment of inertia will accelerate faster.
Step 5: Conclude that since the disk has a smaller moment of inertia, it will reach the bottom of the incline before the ring.

Moment of Inertia – The distribution of mass in an object affects its rotational motion; a lower moment of inertia means less resistance to rolling.
Rolling Motion – Objects rolling down an incline convert potential energy into both translational and rotational kinetic energy.
Energy Conservation – The total mechanical energy (potential + kinetic) is conserved, influencing how quickly objects reach the bottom.