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

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Question: 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?

Options:

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

Correct Answer: Solid sphere

Solution: 

The solid sphere will have a greater translational speed because it has a smaller moment of inertia.

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

Practice Questions

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?
  1. Solid sphere
  2. Hollow sphere
  3. Both will have the same speed
  4. Depends on the mass

Questions & Step-by-Step Solutions

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?
  • 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.
  • Moment of Inertia – The moment of inertia determines how mass is distributed in an object and affects its rotational motion.
  • Energy Conservation – The total mechanical energy (potential + kinetic) is conserved in the absence of air resistance, and the distribution of energy between translational and rotational forms is key.
  • Rolling Motion – Understanding how rolling objects convert potential energy into both translational and rotational kinetic energy.
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