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MHT CET 2025 (21 Apr, Shift 1) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from MHT CET 2025 (21 Apr, Shift 1)

Q60MHT CET 2025 · 21 APR · SHIFT 1Difficult

Moment of Inertia & Radius of Gyration

Three spheres, each of mass ' mm ' and radius ' rr ' are placed as shown in figure. Consider an axis YY′YY', 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′YY' axis is

Figure

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Answer: (c)

  1. Sphere 1: axis is its diameter, 25mr2\frac{2}{5}mr^2.
  2. Spheres 2 and 3: axis is a tangent, 25mr2+mr2=75mr2\frac{2}{5}mr^2 + mr^2 = \frac{7}{5}mr^2 each.
  3. I=25mr2+145mr2=165mr2I = \frac{2}{5}mr^2 + \frac{14}{5}mr^2 = \frac{16}{5}mr^2
  4. So the answer is (c).
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