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BITSAT2015PhysicsRotational MotionActual

A thin rod of length 41 and mass 4 ~m is bent at the points as shown in figure. What is the moment of inertia of the rod about the axis passes through point O and perpendicular to the plane of paper?

Options

  1. AM l² 3
  2. B10 M l² 3
  3. CM l² 12
  4. DM l² 24

Correct answer

B. 10 M l² 3

Step-by-step solution

Total moment of inertia = I ₁+ I ₂+ I ₃+ I ₄=2 I ₁+2 I ₂ array l =2 (l₁+l₂ ) I₃=I₁, I₁=I₄ ] Now, I₂=I₃= M I² 3 array Using parallel axes theorem, we have array l I = I _ CM + Mx ² and x = l²+ l² 4 I ₁= I ₄= M l² 12 + M [ l²+ ( l 2 )² ]² array Putting all values we get Moment of inertia, I =10 ( Ml ² 3 )

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