Question:

A thin wire of length $l$ and mass $m$ is bent in a form of semicircle. Its moment of inertia about an axis joining its free ends will be

Updated On: Jul 6, 2022
  • $ \frac {2ml^2}{\pi^2}$
  • $ ml^2$
  • $ \frac {ml^2} {2}$
  • $\frac {ml^2}{2\pi^2}$
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The Correct Option is D

Solution and Explanation

Here $\pi r = l \, i.e., \, r = \frac{l}{\pi}$ M.O.I. = $\frac{Mr^2}{2} = \frac{Ml^2}{2 \pi^2}$
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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.