An iron load of $2 \mathrm{~kg}$ is suspended in air from the free end of a sonometer wire of length $1…

An iron load of $2 \mathrm{~kg}$ is suspended in air from the free end of a sonometer wire of length $1 \mathrm{~m}$. A tuning fork of frequency $256 \mathrm{~Hz}$, is in resonance with $\frac{1}{\sqrt{7}}$ times the length of the sonometer wire. If the load is immensed in water, the length of the wire in metre that will be in resonance with the same tuning fork is $($ Specific gravity of iron $=8)$
  1. $\sqrt{8}$
  2. $\sqrt{6}$
  3. $\frac{1}{\sqrt{6}}$
  4. $\frac{1}{\sqrt{8}}$

Solution

We know $I \propto \sqrt{T}$ $ \therefore \quad \frac{I_{\text {air }}}{I_{\text {water }}}=\sqrt{\frac{T_{\text {air }}}{T_{\text {water }}}} $ $\begin{array}{llrl}\text { But specific gravity } 8 & =\frac{T_{\text {air }}}{T_{\text {air }}-T_{\text {water }}} \\ \Rightarrow & T_{\text {water }} =\frac{7}{8} T_{\text {air }} \\ \therefore & \frac{l_{\text {air }}}{l_{\text {water }}} =\sqrt{\frac{8}{7}} \\ \text { But } & l_{\text {air }} =\frac{1}{\sqrt{7}} l \text { (given) } \\ \therefore & l_{\text {water }} =\frac{1}{\sqrt{8}} l\end{array}$

Asked in: AP EAMCET 2004

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