Oscillations

JEE Main level, single correct, medium

137 of 194

Question 137 of 194

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 :

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Answer: (B) 1.9 Hz

No contact ⇒N=0\Rightarrow N=0

⇒amax=g=w2A\Rightarrow {a}_{max}=g={w}^{2}A

w=gAw=\sqrt{\dfrac{g}{A}}=100.07=\sqrt{\dfrac{10}{0.07}}

f=w2π=1000712π=1.9f=\dfrac{w}{2\pi }=\sqrt{\dfrac{1000}{7}}\dfrac{1}{2\pi }=1.9 Hz

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