Q142 / 160 · TS EAMCET 2004 · Physics
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 $=8)$
- A$\sqrt{8}$
- B$\sqrt{6}$
- C$\frac{1}{\sqrt{6}}$
- Correct answerD$\frac{1}{\sqrt{8}}$
Solution
We know $I \propto \sqrt{T}$
$$
\therefore \quad \frac{I_{\text {air }}}{I_{\text {water }}}=\sqrt{\frac{T_{\text {air }}}{T_{\text {water }}}}
$$ $\begin{array}{llrl}\text { But specific gravity } 8 & =\frac{T_{\text {air }}}{T_{\text {air }}-T_{\text {water }}} \\ \Rightarrow & T_{\text {water }} =\frac{7}{8} T_{\text {air }} \\ \therefore & \frac{l_{\text {air }}}{l_{\text {water }}} =\sqrt{\frac{8}{7}} \\ \text { But } & l_{\text {air }} =\frac{1}{\sqrt{7}} l \text { (given) } \\ \therefore & l_{\text {water }} =\frac{1}{\sqrt{8}} l\end{array}$
Hence, the correct answer is option: 'D'.