In an engine the piston undergoes vertical simple harmonic motion...

In an engine the piston undergoes vertical simple harmonic motion with amplitude 7cm. 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 :

Options

A0.7 Hz
B1.9 Hz
C1.2 Hz
D0.1 Hz

Correct answer

B. 1.9 Hz

Step-by-step solution

No contact

⇒ N = 0

⇒ {a}_\max = g = {w}^{2}A

w = \sqrt{\dfrac{g}{A}}

= \sqrt{\dfrac{10}{0.07}}

f = \dfrac{w}{2\pi} = \sqrt{\dfrac{1000}{7}}\dfrac{1}{2\pi} = 1.9

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