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MHT CET 2025 (19 Apr, Shift 1) · Simple Pendulum

Simple Pendulum question from MHT CET 2025 (19 Apr, Shift 1)

Q25MHT CET 2025 · 19 APR · SHIFT 1Medium

Simple Pendulum

' PP ' and ' QQ ' are fixed points in same plane and mass ' mm ' is tied by string as shown in figure. If the mass is displaced slightly out of this plane and released, it will oscillate with time period (PQ=2d,PR=QR=L)(g=(PQ = 2d, PR = QR = L)(g = gravitational acceleration)

Figure

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Answer: (c)

PQddLL√(L²−d²)R
  1. Displaced out of the plane, the mass swings about the line PQPQ.
  2. Effective length = distance of RR from PQPQ: leff=L2−d2l_{eff} = \sqrt{L^2 - d^2}.
  3. T=2πleffg=2π(L2−d2)1/2gT = 2\pi\sqrt{\frac{l_{eff}}{g}} = 2\pi\sqrt{\frac{(L^2 - d^2)^{1/2}}{g}}
  4. So the answer is (c).
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