Question:

Which of the following has the highest moment of inertia when each of them has the same mass and the same radius?

Updated On: Jul 7, 2022
  • A ring about any of its diameter
  • A disc about any of its diameter
  • A hollow sphere about any of its diameter
  • A solid sphere about any of its diameter
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The Correct Option is C

Solution and Explanation

Let $M$ and $R$ be the mass and radius respectively. Moment of inertia of a ring about any of its diameter is $I_{\text{ring}} =\frac{1}{2}MR^2$ Moment of inertia of a disc about any of its diameter is $I_{\text{disc}} =\frac{1}{4}MR^2$ Moment of inertia of a hollow sphere about any of its diameter is $I_{\text{hollow sphere}} =\frac{2}{3}MR^2$ Moment of inertia of a solid sphere about any of its diameter is $I_{\text{solid sphere}} =\frac{2}{5}MR^2$ Thus, $I_{\text{hollow sphere}}$ Is largest.
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Concepts Used:

System of Particles and Rotational Motion

  1. The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
  2. The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
  3. The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.