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A solid cylinder and a hollow cylinder of the same mass and radius are released

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Question: A solid cylinder and a hollow cylinder of the same mass and radius are released from rest at the same height. Which one will have a greater speed at the bottom?

Options:

  1. Solid cylinder
  2. Hollow cylinder
  3. Both have the same speed
  4. Depends on the mass

Correct Answer: Solid cylinder

Solution: 

The solid cylinder has a smaller moment of inertia compared to the hollow cylinder, thus it will have a greater speed at the bottom.

A solid cylinder and a hollow cylinder of the same mass and radius are released

Practice Questions

Q1
A solid cylinder and a hollow cylinder of the same mass and radius are released from rest at the same height. Which one will have a greater speed at the bottom?
  1. Solid cylinder
  2. Hollow cylinder
  3. Both have the same speed
  4. Depends on the mass

Questions & Step-by-Step Solutions

A solid cylinder and a hollow cylinder of the same mass and radius are released from rest at the same height. Which one will have a greater speed at the bottom?
Correct Answer: Solid cylinder
  • Step 1: Understand that both cylinders are released from the same height and have the same mass and radius.
  • Step 2: Know that when they roll down, 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 cylinder has a smaller moment of inertia, which means it spins more easily compared to the hollow cylinder.
  • Step 5: Since the solid cylinder can convert more of its potential energy into translational kinetic energy, it will move faster.
  • Step 6: Conclude that the solid cylinder will have a greater speed at the bottom than the hollow cylinder.
  • Moment of Inertia – The moment of inertia determines how mass is distributed in an object and affects its rotational motion.
  • Conservation of Energy – The total mechanical energy (potential + kinetic) is conserved in the absence of non-conservative forces.
  • Rolling Motion – Objects rolling down an incline convert potential energy into both translational and rotational kinetic energy.
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