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

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Question: A solid cylinder and a hollow cylinder of the same mass and radius are rolling down an incline. Which one reaches the bottom first? (2023)

Options:

  1. Solid cylinder
  2. Hollow cylinder
  3. Both reach at the same time
  4. Depends on the angle of incline

Correct Answer: Solid cylinder

Exam Year: 2023

Solution: 

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

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

Practice Questions

Q1
A solid cylinder and a hollow cylinder of the same mass and radius are rolling down an incline. Which one reaches the bottom first? (2023)
  1. Solid cylinder
  2. Hollow cylinder
  3. Both reach at the same time
  4. Depends on the angle of incline

Questions & Step-by-Step Solutions

A solid cylinder and a hollow cylinder of the same mass and radius are rolling down an incline. Which one reaches the bottom first? (2023)
  • Step 1: Understand that both cylinders 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 solid cylinder has a smaller moment of inertia than a hollow cylinder.
  • Step 4: Realize that a smaller moment of inertia means the solid cylinder can convert more of its potential energy into translational kinetic energy (moving down) rather than rotational kinetic energy (spinning).
  • Step 5: Conclude that since the solid cylinder accelerates faster due to its smaller moment of inertia, it will reach the bottom of the incline before the hollow cylinder.
  • Moment of Inertia – The moment of inertia is a measure of an object's resistance to changes in its rotation. A solid cylinder has a lower moment of inertia compared to a hollow cylinder of the same mass and radius.
  • Rolling Motion – Rolling motion involves both translational and rotational motion. The acceleration of rolling objects depends on their moment of inertia.
  • Acceleration on Incline – The acceleration of an object rolling down an incline is influenced by its moment of inertia, affecting how quickly it reaches the bottom.
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