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MHT CET 2024 (15 May, Shift 1) · Velocity & Acceleration in SHM

Velocity & Acceleration in SHM question from MHT CET 2024 (15 May, Shift 1)

Q36MHT CET 2024 · 15 MAY · SHIFT 1Medium

Velocity & Acceleration in SHM

A horizontal platform with a small object placed on it executes a linear S.H.M. in the vertical direction. The amplitude of oscillation is 40 cm. What should be the least period of these oscillations, so that the object is not detached from the platform? [Take g=10 m/s2g = 10\text{ m/s}^2]

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Answer: (c)

  1. The object stays on the platform if the largest downward acceleration ω2A≤g\omega^2 A \le g.
  2. Limit: ω2=gA=100.4=25⇒ω=5 rad/s\omega^2 = \dfrac{g}{A} = \dfrac{10}{0.4} = 25 \Rightarrow \omega = 5\text{ rad/s}
  3. Tmin=2πω=2π5=0.4π sT_{min} = \dfrac{2\pi}{\omega} = \dfrac{2\pi}{5} = 0.4\pi\text{ s}
  4. So the answer is (c) 0.4π s0.4\pi\text{ s}.
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