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MHT CET202521 Apr 2025Morning ShiftPhysicsRotational MotionActual

Three spheres, each of mass ' m ' and radius ' r ' are placed as shown in figure. Consider an axis YY ^1 , which is touching two spheres and passing through the diameter of third sphere. The moment of inertia of the system consisting of these three spheres about YY ^1 axis is

Options

  1. A7 5 mr ^2
  2. B2 5 mr ^2
  3. C16 5 mr ^2
  4. Dmr ^2 2

Correct answer

C. 16 5 mr ^2

Step-by-step solution

Moment of inertia of Sphere 1: Since axis YY ^1 passes through its diameter, I₁ = 2 5 mr^2 . Moment of inertia of Sphere 2 and Sphere 3: The axis is tangential to both spheres at distance r from their centers. Using the parallel axis theorem, I₂ = I₃ = 2 5 mr^2 + mr^2 = 7 5 mr^2 . Summing the contributions: I_ total = I₁ + I₂ + I₃ = 2 5 mr^2 + 7 5 mr^2 + 7 5 mr^2 = 16 5 mr^2 . The result corresponds to option C .

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