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A large horizontal surface moves up and down in S.H.M. with an amplitude of \(1 \mathrm{~cm}\). If a mass of \(10 \mathrm{~kg}\) (which is placed on the surface) is to remain continuously in contact with it, the maximum frequency of S.H.M. will be
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The correct answer is:
\(5 \mathrm{~Hz}\)
Here, \(a=1 \mathrm{~cm}=0.01 \mathrm{~m}\); The mass will remain in contact with surface, if
\(m g=m \omega^2 a \text { or } \omega=\sqrt{g / a}\)
\(\begin{aligned}
& \text { or } 2 \pi v=\sqrt{g / a} \text { or } v=\frac{1}{2 \pi} \sqrt{\frac{g}{a}} \\
& v=\frac{7}{2 \times 22} \sqrt{\frac{980}{1}}=4.9 \mathrm{~s}^{-1}=5 \mathrm{~Hz}
\end{aligned}\)
\(m g=m \omega^2 a \text { or } \omega=\sqrt{g / a}\)
\(\begin{aligned}
& \text { or } 2 \pi v=\sqrt{g / a} \text { or } v=\frac{1}{2 \pi} \sqrt{\frac{g}{a}} \\
& v=\frac{7}{2 \times 22} \sqrt{\frac{980}{1}}=4.9 \mathrm{~s}^{-1}=5 \mathrm{~Hz}
\end{aligned}\)
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