Question:

Four small objects each of mass m are fixed at the corners of a rectangular wire-frame of negligible mass and of sides aa and b(a>b)b (a > b). If the wire frame is now rotated about an axis passing along the side of length b, then the moment of inertia of the system for this axis of rotation is

Updated On: May 28, 2024
  • 2 ma22\,ma^2
  • 4 ma24\,ma^2
  • 2 m(a2+b2)2\,m(a^2 + b^2)
  • 2 m(a2−b2)2\,m(a^2 - b^2)
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The Correct Option is A

Solution and Explanation

The given situation can be shown as



Moment of inertia of the system about side of length bb say CDC D is
== M.I. of mass at AA about CD+M.I.C D+M . I . of mass at BB about CD+M.ICD + M . I. of mass at CC about CDCD ++ M.I. of mass ot DD about CDC D
=m(a)2+m(a)2+m(0)2+m(0)2=m(a)^{2}+m(a)^{2}+m(0)^{2}+m(0)^{2}
=2 ma2=2\, m a^{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.