If a solid sphere and a hollow sphere of the same mass and radius roll down an i

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Question: If a solid sphere and a hollow sphere of the same mass and radius roll down an incline, which will reach the bottom first?

Options:

Correct Answer: Solid sphere

Solution:

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

If a solid sphere and a hollow sphere of the same mass and radius roll down an incline, which will reach the bottom first?

If a solid sphere and a hollow sphere of the same mass and radius roll down an incline, which will reach the bottom first?

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: The solid sphere has a lower moment of inertia compared to the hollow sphere. This means it can roll down the incline more easily.
Step 5: Since the solid sphere accelerates faster due to its lower moment of inertia, it will reach the bottom of the incline first.

Moment of Inertia – The distribution of mass in an object affects its rotational motion; a lower moment of inertia means less resistance to acceleration.
Rolling Motion – Objects rolling down an incline experience both translational and rotational motion, which influences their acceleration.
Acceleration on Inclines – The acceleration of rolling objects down an incline is influenced by their moment of inertia and mass distribution.