In an experiment with sonometer when a mass of $180\,g$ is attached to the string, it vibrates with fundamental frequency of $30\,Hz$. When a mass $m$ is attached, the string vibrates with fundamental frequency of $50\,Hz$. The value of $m$ is $.........\,g$.
JEE MAIN 2023, Medium
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$f =\frac{1}{2 \ell} \sqrt{\frac{ T }{\mu}} \quad( T : \text { Tension })$
$\frac{ f _2}{ f _1}=\sqrt{\frac{ T _2}{ T _1}}$
$\left(\frac{50}{30}\right)^2=\frac{ mg }{180 g } \Rightarrow m =\frac{25}{9} \times 180=500 \text { gram }$
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