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A ball rolls without slipping on a flat surface. If the ball's radius is doubled

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Question: A ball rolls without slipping on a flat surface. If the ball\'s radius is doubled while keeping its mass constant, how does its moment of inertia change?

Options:

  1. Increases by a factor of 2
  2. Increases by a factor of 4
  3. Increases by a factor of 8
  4. Remains the same

Correct Answer: Increases by a factor of 4

Solution: 

The moment of inertia of a solid sphere is (2/5)MR^2. If the radius is doubled, the moment of inertia increases by a factor of 4.

A ball rolls without slipping on a flat surface. If the ball's radius is doubled

Practice Questions

Q1
A ball rolls without slipping on a flat surface. If the ball's radius is doubled while keeping its mass constant, how does its moment of inertia change?
  1. Increases by a factor of 2
  2. Increases by a factor of 4
  3. Increases by a factor of 8
  4. Remains the same

Questions & Step-by-Step Solutions

A ball rolls without slipping on a flat surface. If the ball's radius is doubled while keeping its mass constant, how does its moment of inertia change?
Correct Answer: Moment of inertia increases by a factor of 4.
  • Step 1: Understand what moment of inertia is. It is a measure of how difficult it is to change the rotation of an object.
  • Step 2: Know the formula for the moment of inertia of a solid sphere, which is (2/5)MR^2, where M is mass and R is radius.
  • Step 3: Identify that the mass (M) of the ball remains constant in this problem.
  • Step 4: Recognize that if the radius (R) is doubled, we replace R with 2R in the formula.
  • Step 5: Substitute 2R into the moment of inertia formula: Moment of inertia = (2/5)M(2R)^2.
  • Step 6: Calculate (2R)^2, which equals 4R^2.
  • Step 7: Now the moment of inertia becomes (2/5)M(4R^2) = (8/5)MR^2.
  • Step 8: Compare the new moment of inertia (8/5)MR^2 with the original (2/5)MR^2. The new moment of inertia is 4 times the original moment of inertia.
  • Moment of Inertia – The moment of inertia is a measure of an object's resistance to changes in its rotation, depending on its mass distribution relative to the axis of rotation.
  • Effect of Radius on Moment of Inertia – The moment of inertia for a solid sphere is proportional to the square of its radius, meaning if the radius is doubled, the moment of inertia increases by a factor of four.
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