Question

A $0.1kg$ mass is suspended from a wire of negligible mass. The length of the wire is $1m$ and its cross-sectional area is $4.9\times {10}^{-7}{m}^2$. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency $140rad{s}^{-1}$. If the Young's modulus of the material of the wire is $n\times {10}^{9}N{m}^{-2}$, the value of $n$ is

Answer 1

Given,

$\omega =140rad{s}^{-1}$

$areaa=4.9\times {10}^{-7}{m}^2$

$massm=0.1kg$

$lengthL=1m$

$Y=n\times {10}^{9}N{m}^{-2}$

$n=?$

$\omega =\sqrt{\frac{YA}{mL}}$.

$140=\sqrt{\frac{n\times {10}^9\times 4.9\times {10}^{-7}}{0.1\times 1}}$

$n=4$