At the poles of earth, a stretched wire of a given length vibrates in unison with a tuning fork. At the…
At the poles of earth, a stretched wire of a given length vibrates in unison with a tuning fork. At the equator of earth, for same setting, to produce resonance with same fork, the vibrating length of wire
should be decreased.
should be increased.
should be same.
should be three times the original.
Solution
For a string,
Frequency of vibration $n=\frac{1}{2 l} \sqrt{\frac{\mathrm{~T}}{\mathrm{~m}}}$
If $\mathrm{T}=\mathrm{Mg}$, then $\mathrm{n}=\frac{1}{2 l} \sqrt{\frac{\mathrm{Mg}}{\mathrm{m}}}$
If $l_1$ and $g_1$ are the length and acceleration due to gravity at the poles and $l_2$ and $g_2$ at the equator respectively, then if the frequency is the same,
$\begin{array}{ll}
& \mathrm{n}=\frac{1}{2 l_1} \sqrt{\frac{\mathrm{Mg}_1}{\mathrm{~m}}}=\frac{1}{2 l_2} \sqrt{\frac{\mathrm{Mg}_2}{\mathrm{~m}}} \\
\therefore \quad & \frac{\sqrt{\mathrm{~g}_1}}{l_1}=\frac{\sqrt{\mathrm{g}_2}}{l_2} \text { or } \frac{l_2}{l_1}=\sqrt{\frac{\mathrm{g}_2}{\mathrm{~g}_1}} \\
\therefore \quad & \mathrm{~g}_2 \lt \mathrm{g}_1 \\
\therefore \quad & l_2 \lt l_1
\end{array}$