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:

• A. $f =\frac{1}{2 \pi} \sqrt{\frac{ YA }{ mL }}$
• B. $f =\frac{1}{2 \pi} \sqrt{\frac{ YL }{ mA }}$
• C. $f =\frac{1}{2 \pi} \sqrt{\frac{ mA }{ YL }}$
• D. $f =\frac{1}{2 \pi} \sqrt{\frac{ mL }{ YA }}$

Answer 1

Answer: (A)

An elastic wire can be treated as a spring with
$k =\frac{ YA }{\ell}$
$T =2 \pi \sqrt{\frac{ m }{ k }}$
$f =\frac{1}{2 \pi} \sqrt{\frac{ k }{ m }}=\frac{1}{2 \pi} \sqrt{\frac{ YA }{ m \ell}}$