The length of a light string is 1.4 m when the tension on it is 5...

The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N , the length of the string is 1.56 m. The original length of the string is _____ m.

Correct answer

Step-by-step solution

\begin{aligned} & \mathrm{T}=\mathrm{K}\left(\ell-\ell_0\right) \\ & \Rightarrow 5=\mathrm{K}\left(1.4-\ell_0\right) \\ & \Rightarrow 7=\mathrm{K}\left(1.56-\ell_0\right) \\ & \Rightarrow \frac{5}{1.4-\ell_0}=\frac{7}{1.56-\ell_0} \\ & \therefore \ell_0=1 \mathrm{~m}\end{aligned}

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