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A solid sphere and a hollow sphere of the same mass and radius are rolling down

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Question: A solid sphere and a hollow sphere of the same mass and radius are rolling down an incline. Which one will reach the bottom first? (2021)

Options:

  1. Solid sphere
  2. Hollow sphere
  3. Both will reach at the same time
  4. It depends on the angle of incline

Correct Answer: Solid sphere

Exam Year: 2021

Solution: 

The solid sphere has a smaller moment of inertia compared to the hollow sphere, allowing it to accelerate faster down the incline.

A solid sphere and a hollow sphere of the same mass and radius are rolling down

Practice Questions

Q1
A solid sphere and a hollow sphere of the same mass and radius are rolling down an incline. Which one will reach the bottom first? (2021)
  1. Solid sphere
  2. Hollow sphere
  3. Both will reach at the same time
  4. It depends on the angle of incline

Questions & Step-by-Step Solutions

A solid sphere and a hollow sphere of the same mass and radius are rolling down an incline. Which one will reach the bottom first? (2021)
  • Step 1: Understand that both spheres have the same mass and radius.
  • Step 2: Know that when objects roll down an incline, their shape affects how they move.
  • Step 3: Learn about moment of inertia, which is a measure of how difficult it is to change an object's rotation.
  • Step 4: Realize that the solid sphere has a smaller moment of inertia than the hollow sphere.
  • Step 5: Understand that a smaller moment of inertia means the solid sphere can rotate more easily and accelerate faster.
  • Step 6: Conclude that because the solid sphere accelerates faster, it will reach the bottom of the incline first.
  • Moment of Inertia – The moment of inertia is a measure of an object's resistance to changes in its rotation. A lower moment of inertia allows for faster acceleration when rolling.
  • Rolling Motion – Rolling motion involves both translational and rotational kinetic energy. The distribution of mass affects how quickly an object can roll down an incline.
  • Acceleration on Inclines – Objects rolling down an incline accelerate based on their moment of inertia and the gravitational force acting on them.
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