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Three solid spheres each of mass m and diameter d are stuck together such that the lines connecting the centres form an equilateral triangle of side length d . Find the ratio I 0 / I A , where I 0 is the moment of inertia of the system about an axis passing through the centroid and I A is the moment of inertia of the system about an axis passing through the centre of any sphere and perpendicular to the plane of the t

Options

  1. A23 13
  2. B13 15
  3. C13 23
  4. D15 13

Correct answer

C. 13 23

Step-by-step solution

The moment of inertia of the system about the point O is I 0 = 3 2 5 M d 2 2 + M d 3 2 = 13 10 M d 2 The moment of inertia of the system about the point A is I A = 2 2 5 M d 2 2 + M ( d ) 2 + 2 5 M d 2 2 = 23 10 M d 2 So, the ratio = 13 23

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