An object of mass m is suspended at the end of a massless wire of… - Vidyadip

MCQ

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

✓
$f =\frac{1}{2 \pi} \sqrt{\frac{ YA }{ mL }}$
B
$f=\frac{1}{2 \pi} \sqrt{\frac{Y L}{m A}}$
C
$f=\frac{1}{2 \pi} \sqrt{\frac{m A}{Y L}}$
D
$f =\frac{1}{2 \pi} \sqrt{\frac{ mL }{ YA }}$

✓

Answer

Correct option: A.

$f =\frac{1}{2 \pi} \sqrt{\frac{ YA }{ mL }}$

a
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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