Question

Two wires of the same diameter and same material having length $1.2m$ and $2m$, vibrates with the same fundamental frequency. If the shorter wire is stretched by a force of $36kgwt$, then the tension in the longer wire is:

• A. $50kgwt$
• B. $200kgwt$
• C. $100kgwt$
• D. $400kgwt$

Answer 1

Answer: (C)

$100kgwt$

Fundamental frequency of a wire with some applied tension is $\nu =\frac{\sqrt{\frac{T}{\mu }}}{2l}$

Thus, $\frac{\sqrt{\frac{T_1}{\mu }}}{2l_1}=\frac{\sqrt{\frac{T_2}{\mu }}}{2l_2}$

$⟹T_2=T_1\times \frac{l_2^2}{l_1^2}$

$=36\times \frac{2^2}{{1.2}^2}=100kgwt$