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STD 11 - 13. oscillations — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 13. oscillations4 Marks
MCQ
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 ...... $Hz$
  • A
    $0.7$
  • ✓
    $1.9$
  • C
    $1.2$
  • D
    $0.1$
✓

Answer

Correct option: B.
$1.9$
b
Washer contact with piston $\Rightarrow \mathrm{N}=0$

Given Amplitude $\mathrm{A}=7 \mathrm{cm}=0.07 \mathrm{m}$

$a_{\max }=g=\omega^{2} A$

The frequency of piston

$\mathrm{f}=\frac{\omega}{2 \pi}=\sqrt{\frac{\mathrm{g}}{\mathrm{A}}} \frac{1}{2 \pi}=\sqrt{\frac{1000}{7}} \frac{1}{2 \pi}=1.9 \mathrm{Hz}$

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