A cable breaks if stretched by more than $2$ mm. It is cut into two equal parts. How much either part can be stretched without breaking?

0.25

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0.5

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Solution

The correct option is C $1$ mm
$\begin{matrix} P = stress E = young's modulus \end{matrix}$

$\begin{matrix} Δ L = \frac{P L}{A E} \Rightarrow Δ L α L \frac{Δ L_{1}}{Δ L_{2}} = \frac{L_{1}}{L_{2}} since Δ L_{1} = 2 m m \frac{2 m m}{Δ L_{2}} = \frac{L_{1}}{L_{1} / 2} \end{matrix}$

$\begin{matrix} \Rightarrow \frac{2 m m}{Δ L_{2}} = 2 \Rightarrow Δ L_{2} = 1mm hence , now each part is stretched by 1mm \end{matrix}$

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