8.Mechanical Properties of Solids
medium

The proportional limit of steel is $8 \times 10^8 \,N / m ^2$ and its Young's modulus is $2 \times 10^{11} \,N / m ^2$. The maximum elongation, a one metre long steel wire can be given without exceeding the elastic limit is ...... $mm$

A

$2$

B

$4$

C

$1$

D

$8$

Solution

(b)

At proportional limit

Stress $\propto$ strain

Stress $=Y \times$ strain   $\{Y=$ Young's Modulus $\}$

Stress $=Y \times \frac{\Delta L}{L}$  $\left\{\begin{array}{l}\text { Stress }=8 \times 10^8 \,N / m ^2 \\ Y=2 \times 10^{11} \,N / m ^2 \\ L=1 \,m \end{array}\right.$

Substituting values

$\frac{8 \times 10^8 \times 1}{2 \times 10^{11}}=\Delta L$

$4 \,mm=\Delta L$

Standard 11
Physics

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