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?
Practice Questions
1 question
Q1
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?
Solid sphere
Hollow sphere
Both reach at the same time
Depends on the angle of incline
The solid sphere has a smaller moment of inertia compared to the hollow sphere, allowing it to accelerate faster down the incline.
Questions & Step-by-step Solutions
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Q
Q: 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?
Solution: The solid sphere has a smaller moment of inertia compared to the hollow sphere, allowing it to accelerate faster down the incline.
Steps: 6
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.
