In an engine the piston undergoes vertical simple harmonic motion… - Vidyadip

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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