At the poles, a stretched wire of a given length vibrates in unison with a tuning fork. At the equator, for same setting to produce resonance with same fork, the
vibrating length of wire

(A)
Frequency of vibration \(\quad \mathrm{n}=\frac{1}{2 \mathrm{e}} \sqrt{\frac{\mathrm{T}}{\mathrm{m}}}\)
If \(\mathrm{T}=\mathrm{Mg}\), then \(\mathrm{n}=\frac{1}{2 \mathrm{e}} \sqrt{\frac{\mathrm{Mg}}{\mathrm{m}}}\)
If \(\ell_{1}\) and \(\mathrm{g}_{1}\) are length and acceleration due to gravity at the pole and \(\ell_{2}\) and \(\mathrm{g}_{2}\) at the equator then, if frequency is same, then
\(n=\frac{1}{2 \ell_{1}} \sqrt{\frac{M g_{1}}{m}}=\frac{1}{2 \ell_{2}} \sqrt{\frac{M g_{2}}{m}}\)
\(\therefore \frac{\sqrt{g_{1}}}{\ell_{1}}=\frac{\sqrt{g_{2}}}{\ell_{2}}\)
or \(\frac{\ell_{2}}{\ell_{1}}=\sqrt{\frac{g_{2}}{g_{1}}}\)
\(\mathrm{g}_{2} < \mathrm{g}_{1} \quad \therefore \ell_{2} < \ell_{1}\)