A solid sphere and a hollow sphere of the same mass and radius are released from rest at the same height. Which one will have a greater translational speed when they reach the ground?
Practice Questions
1 question
Q1
A solid sphere and a hollow sphere of the same mass and radius are released from rest at the same height. Which one will have a greater translational speed when they reach the ground?
Solid sphere
Hollow sphere
Both will have the same speed
Depends on the mass
The solid sphere will have a greater translational speed because it has a smaller moment of inertia.
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 released from rest at the same height. Which one will have a greater translational speed when they reach the ground?
Solution: The solid sphere will have a greater translational speed because it has a smaller moment of inertia.
Steps: 6
Step 1: Understand that both spheres are released from the same height and have the same mass and radius.
Step 2: Know that when they fall, they convert potential energy into kinetic energy.
Step 3: Recognize that kinetic energy has two parts: translational (movement) and rotational (spinning).
Step 4: The solid sphere has a smaller moment of inertia compared to the hollow sphere, meaning it spins less for the same amount of energy.
Step 5: Since the solid sphere uses more of its energy for translational speed (moving downwards) and less for rotation, it will reach the ground faster.
Step 6: Conclude that the solid sphere will have a greater translational speed when they reach the ground.
