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

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Question: If a hollow cylinder and a solid 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.

If a hollow cylinder and a solid cylinder of the same mass and radius roll down the same incline, which one reaches the bottom first?

If a hollow cylinder and a solid 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, they have both translational (moving down) and rotational (spinning) motion.
Step 3: Learn about moment of inertia, which is a measure of how difficult it is to change an object's rotation. A smaller moment of inertia means it's easier to roll.
Step 4: Compare the moment of inertia of the solid cylinder and the hollow cylinder. The solid cylinder has a smaller moment of inertia than the hollow cylinder.
Step 5: Since the solid cylinder has a smaller moment of inertia, it can convert more of its potential energy into translational kinetic energy, allowing it to roll down faster.
Step 6: Conclude that the solid cylinder reaches the bottom of the incline first.

Moment of Inertia – The moment of inertia is a measure of an object's resistance to changes in its rotation. A solid cylinder has a lower moment of inertia than a hollow cylinder, affecting their acceleration down an incline.
Rolling Motion – Rolling motion involves both translational and rotational kinetic energy. The distribution of mass affects how quickly an object can roll down an incline.
Energy Conservation – As the cylinders roll down the incline, potential energy is converted into kinetic energy, which is divided into translational and rotational forms.