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JEE Main 2026 (4 Apr, Shift 2) · Other SHM Systems

Other SHM Systems question from JEE Main 2026 (4 Apr, Shift 2)

Q3JEE Main 2026 · 4 APR · SHIFT 2Medium

Other SHM Systems

A uniform disc of radius RR and mass MM is free to oscillate about the axis AA as shown in the figure. For small oscillations the time period is ______.

(g is acceleration due to gravity)

Figure

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Answer: (a)

  1. Axis A is a tangent in the plane of the disc. About a diameter I=MR24I = \frac{MR^2}{4}; parallel axes: IA=MR24+MR2=5MR24I_A = \frac{MR^2}{4} + MR^2 = \frac{5MR^2}{4}.
  2. Physical pendulum: T=2πIAMgdT = 2\pi\sqrt{\frac{I_A}{Mgd}} with d=Rd = R.
  3. T=2π5MR2/4MgR=2π5R4gT = 2\pi\sqrt{\frac{5MR^2/4}{MgR}} = 2\pi\sqrt{\frac{5R}{4g}}, answer (a).
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