A solid sphere and a hollow sphere of the same mass and radius are rolling down

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

Options:

Correct Answer: Solid sphere

Solution:

The solid sphere has a smaller moment of inertia compared to the hollow sphere, allowing it to accelerate faster down the incline.

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

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

Correct Answer: Solid sphere

Step 1: Understand that both spheres 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 lower moment of inertia means it can rotate more easily.
Step 4: Recognize that the solid sphere has a smaller moment of inertia than the hollow sphere.
Step 5: Since the solid sphere can rotate more easily, it will accelerate faster down the incline.
Step 6: Conclude that the solid sphere will reach the bottom of the incline before the hollow sphere.

Moment of Inertia – The solid sphere has a lower moment of inertia than the hollow sphere, which affects how quickly each can accelerate when rolling.
Rolling Motion – Understanding the dynamics of rolling objects, including the relationship between translational and rotational motion.
Acceleration on Inclines – The effect of gravitational force and the incline angle on the acceleration of rolling objects.