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

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

Options:

Correct Answer: Solid sphere

Solution:

The solid sphere has a smaller moment of inertia compared to the hollow sphere, thus it accelerates faster and reaches the bottom first.

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

If a hollow sphere and a solid sphere of the same mass and radius roll down the same incline, which one reaches 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 forward) 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 solid sphere has a smaller moment of inertia than a hollow sphere.
Step 4: Realize that a smaller moment of inertia means the solid sphere can convert more of its potential energy into translational kinetic energy (forward motion) rather than rotational kinetic energy (spinning).
Step 5: Conclude that since the solid sphere accelerates faster due to its smaller 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 allows for faster acceleration when rolling.
Rolling Motion – Understanding the difference between translational and rotational motion is crucial for analyzing objects that roll down an incline.
Energy Conservation – The conversion of potential energy to kinetic energy (both translational and rotational) plays a key role in determining which object reaches the bottom first.