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  • A block rides on a piston that is moving vertically with simple harmonic motion. The maximum speed of the piston is <img alt="4 \mathrm{~m} / \mathrm{s}" src="https://entrancecorner.oncodecogs.com/

A block rides on a piston that is moving vertically with simple harmonic motion. The maximum speed of the piston is 4 \mathrm{~m} / \mathrm{s}. We need to determine the amplitude of motion at which the block and piston will separate.
\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)

Option: 1

160 \, \mathrm{cm}


Option: 2

150\, \mathrm{cm}


Option: 3

180 \mathrm{~cm}


Option: 4

170 \mathrm{~cm}


Answers (1)

best_answer

Let A be amplitude
Now, maximum speed of piston =4 \mathrm{~m} / \mathrm{s}

                     \therefore \omega \mathrm{A}=4 \mathrm{~m} / \mathrm{s}

 If  \omega^2 \mathrm{~A}=\mathrm{g}

then they will separate.

\begin{aligned} & \Rightarrow 4 \times \omega=\mathrm{g} \\ & \Rightarrow \omega=2.5 \mathrm{rad} / \mathrm{sec} \\ & \therefore A=\frac{4}{2.5} \mathrm{~m}=160 \mathrm{~cm} \end{aligned}

Posted by

sudhir.kumar

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