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MHT CET20249 May 2024Morning ShiftPhysicsRotational MotionActual

The moment of inertia of thin square plate PQRS of uniform thickness, about an axis passing through centre ' O ' and perpendicular to the plane of the plate is ( I ₁, I ₂, I ₃, I ₄ . are respectively the moments of inertia about axis 1,2,3,4 which are in the plane of the plate as shown in figure)

Options

  1. AI ₁+ I ₂+ I ₃
  2. BI ₁+ I ₃+ I ₄
  3. CI ₁+ I ₂+ I ₃+ I ₄
  4. DI ₁+ I ₃

Correct answer

D. I ₁+ I ₃

Step-by-step solution

Axis of I₁ and I₂ and that of I₃ and I₄ are pependicular to each other. By theorem of perpendicular axis, I = I ₁+ I ₂ or I = I ₃+ I ₄...(i) As it is a square, I ₁= I ₂ and I ₃= I ₄ From (i), aligned & I ₁= I ₂= I 2 & I ₃= I ₄= I 2 aligned I ₃= I ₁ Momentof inertia of the plate = I = I ₁+ I ₃

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