Question:

The moment of inertia of a disc of mass $M$ and radius $R$ about an axis, which is tangential to the circumference of the disc and parallel to its diameter is

Updated On: Jul 5, 2022
  • $\frac{3}{2}MR^2$
  • $\frac{2}{3}MR^2$
  • $\frac{5}{4}MR^2$
  • $\frac {4}{5}MR^2$
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The Correct Option is C

Solution and Explanation

The moment of inertia of a disc about its diameter (i.e. $z$ axis) is $I_{0}=\frac{MR^{2}}{4}$ $\therefore$ According to parallel axis theorem, moment of inertia about the required axis (i.e. z' axis) is
$I=I_{0}+MR^{2}$ $=\frac{MR^{2}}{4}+MR^{2}=\frac{5MR^{2}}{4}$
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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.