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If a string, suspended from the ceilling is given a downward force $F_1$, its length becomes $L_1$, Its length is $L_2$, if the downward force is $\mathrm{F}_2$. What is its actual length?
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$\frac{\mathrm{F}_2 \mathrm{~L}_1-\mathrm{F}_1 \mathrm{~L}_2}{\mathrm{~F}_2-\mathrm{F}_1}$
$\begin{aligned} &\left(L_1-L\right)=\frac{F_1 L}{A y} ; L_2-L=\frac{F_2 L}{A y} \\ \Rightarrow & \frac{L_1-L}{L_2-L}=\frac{F_1}{F_2} \Rightarrow F_2 L_1-F_2 L=F_1 L_2-F_1 L \Rightarrow L=\frac{F_2 L_1-F_1 L_2}{F_2-F_1} \end{aligned}$
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