An object of mass $m$ is suspended at the end of a massless wire of length $L$ and area of cross$-$section, $A$. Young modulus of the material of the wire is $Y$. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is
JEE MAIN 2020, Medium
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An elastic wire can be treated as a spring with
$K =\frac{ Y A }{\ell}$
$T =2 \pi \sqrt{\frac{ m }{ k }}$
$f=\frac{1}{2 \pi} \sqrt{\frac{k}{m}}=\frac{1}{2 \pi} \sqrt{\frac{Y A}{m \ell}}$
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