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KVPY2015PhysicsRotational Motion

The moments of inertia of a non-uniform circular disc (of mass M and radius R ) about four mutually perpendicular tangents AB , BC CD , DA are I₁, I₂, I₃ and I₄ respectively (the square ABCD circumscribes the circle.) The distance of the center of mass of the disc from its geometrical center is given by.

Options

  1. A1 4 M R (I₃-I₃ )²+ (I₂-I₄ )²
  2. B1 12 M R (I₃-I₃ )²+ (I₂-I₄ )²
  3. C1 3 M R (I₁-I₂ )²+ (I₃-I₄ )²
  4. D1 2 M R (I₁+I₃ )²+ (I₂+I₄ )²

Correct answer

A. 1 4 M R (I₃-I₃ )²+ (I₂-I₄ )²

Step-by-step solution

array l I₁=I_ c m +M(R-y)² I₃=I_ c m +M(R+y)² array So I₃-I₁=M [(R+y)²-(R-y)² same as I₄-I₂=M [(R+x)²-(R-x)² ] Ву Distance of CM from center of disc = x²+y² = 1 4 M R (I₃-I₃ )²+ (I₂-I₄ )²

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