A solid cylinder and a hollow cylinder of the same mass and radius roll down the

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Question: A solid cylinder and a hollow cylinder of the same mass and radius roll down the same incline. Which one reaches the bottom first?

Options:

Correct Answer: Solid cylinder

Solution:

The solid cylinder reaches the bottom first because it has a smaller moment of inertia compared to the hollow cylinder.

A solid cylinder and a hollow cylinder of the same mass and radius roll down the same incline. Which one reaches the bottom first?

A solid cylinder and a hollow cylinder of the same mass and radius roll down the same incline. Which one reaches the bottom first?

Step 1: Understand that both cylinders have the same mass and radius.
Step 2: Know that when objects roll down an incline, their shape affects how they move.
Step 3: Learn about 'moment of inertia,' which is a measure of how difficult it is to change an object's rotation.
Step 4: Realize that a solid cylinder has a smaller moment of inertia than a hollow cylinder.
Step 5: Understand that a smaller moment of inertia means the solid cylinder can roll down the incline faster.
Step 6: Conclude that the solid cylinder will reach the bottom of the incline before the hollow cylinder.

Moment of Inertia – The distribution of mass in an object affects its rotational motion; a lower moment of inertia allows for faster acceleration down an incline.
Rolling Motion – Objects rolling down an incline experience both translational and rotational motion, which influences their speed based on their moment of inertia.
Energy Conservation – The conversion of potential energy to kinetic energy (both translational and rotational) determines how quickly an object reaches the bottom of an incline.