An object of mass m is suspended at the end of a massless wire of length L and area of cross-section,
Question:
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:
Correct Option: 1
Solution:
(1) An elastic wire can be treated as a spring and its spring constant.
$k=\frac{Y A}{L}$ $\left[\because Y=\frac{F}{A} / \frac{\Delta l}{l_{0}}\right]$
Frequency of oscillation,
$f=\frac{1}{2 \pi} \sqrt{\frac{k}{m}}=\frac{1}{2 \pi} \sqrt{\frac{Y A}{m L}}$
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