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JEE Main 2016 (10 Apr, Shift 1) · Velocity & Acceleration in SHM

Velocity & Acceleration in SHM question from JEE Main 2016 (10 Apr, Shift 1)

Q70JEE Main 2016 · 10 APR · SHIFT 1Medium

Velocity & Acceleration in SHM

In an engine the piston undergoes vertical simple harmonic motion with amplitude 7 cm. A washer rests on top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer no longer stays in contact with the piston, is close to:

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Answer: (d)

  1. The washer loses contact when ω2A=g\omega^2 A = g.
  2. ω=gA=100.07≈11.95 rad/s\omega = \sqrt{\dfrac{g}{A}} = \sqrt{\dfrac{10}{0.07}} \approx 11.95\text{ rad/s}
  3. f=ω2π=11.956.28≈1.9 Hzf = \dfrac{\omega}{2\pi} = \dfrac{11.95}{6.28} \approx 1.9\text{ Hz}
  4. So the answer is (d) 1.9 Hz.
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