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If a solid sphere and a solid cylinder of the same mass and radius are released

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Question: If a solid sphere and a solid cylinder of the same mass and radius are released from rest at the same height, which will have a greater speed at the bottom?

Options:

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

Correct Answer: Both have the same speed

Solution: 

Both will have the same speed at the bottom due to conservation of energy, as they start from the same height.

If a solid sphere and a solid cylinder of the same mass and radius are released

Practice Questions

Q1
If a solid sphere and a solid cylinder of the same mass and radius are released from rest at the same height, which will have a greater speed at the bottom?
  1. Solid sphere
  2. Solid cylinder
  3. Both have the same speed
  4. Depends on the mass

Questions & Step-by-Step Solutions

If a solid sphere and a solid cylinder of the same mass and radius are released from rest at the same height, which will have a greater speed at the bottom?
Correct Answer: Both will have the same speed at the bottom.
  • Step 1: Understand that both the solid sphere and the solid cylinder are released from the same height.
  • Step 2: Recognize that they both have the same mass and radius.
  • Step 3: Remember the principle of conservation of energy, which states that energy cannot be created or destroyed, only transformed.
  • Step 4: When the objects are at the top, they have potential energy due to their height.
  • Step 5: As they fall, this potential energy is converted into kinetic energy (the energy of motion).
  • Step 6: Since both objects start from the same height, they will have the same amount of potential energy at the top.
  • Step 7: When they reach the bottom, all of that potential energy will have been converted into kinetic energy.
  • Step 8: Therefore, both the solid sphere and the solid cylinder will have the same speed at the bottom.
  • Conservation of Energy – The principle that the total energy in a closed system remains constant; potential energy converts to kinetic energy as the objects fall.
  • Moment of Inertia – The distribution of mass in an object affects its rotational motion, which is relevant when considering how different shapes (sphere vs. cylinder) roll down an incline.
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