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MHT CET 2023 (14 May, Shift 2) · Spring Systems

Spring Systems question from MHT CET 2023 (14 May, Shift 2)

Q54MHT CET 2023 · 14 MAY · SHIFT 2Medium

Spring Systems

A uniform circular disc of mass 12 kg12\text{ kg} is held by two identical springs. When the disc is slightly pressed down and released, it executes S.H.M. of period 2 second. The force constant of each spring is (nearly) (Take π2=10\pi^2 = 10)

Figure

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Answer: (c)

  1. The two springs support the disc in parallel: keff=2kk_{eff} = 2k.
  2. T=2πm2k⇒k=2π2mT2T = 2\pi\sqrt{\frac{m}{2k}} \Rightarrow k = \frac{2\pi^2 m}{T^2}
  3. k=2×10×124=60k = \frac{2\times10\times12}{4} = 60 N/m
  4. So the answer is (c).
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