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?
Practice Questions
1 question
Q1
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?
Hollow sphere
Solid 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, thus it accelerates faster and reaches the bottom first.
Questions & Step-by-step Solutions
1 item
Q
Q: 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?
Solution: The solid sphere has a smaller moment of inertia compared to the hollow sphere, thus it accelerates faster and reaches the bottom first.
Steps: 5
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.
