The maximum elongation of a steel wire of 1 ~m length if the elas… - Vidyadip

MCQ

The maximum elongation of a steel wire of $1 \mathrm{~m}$ length if the elastic limit of steel and its Young's modulus, respectively, are $8 \times 10^8 \mathrm{~N} \mathrm{~m}^{-2}$ and $2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$, is:

A
$0.4 \mathrm{~mm}$
B
$40 \mathrm{~mm}$
C
$8 \mathrm{~mm}$
✓
$4 \mathrm{~mm}$

✓

Answer

Correct option: D.

$4 \mathrm{~mm}$

d
In the case for maximum elongation,

Stress $=$ Elastic limit

$\delta_{\text {max }}=\frac{\sigma_{\text {elastlc }} \times L}{\text { Young's modulus }}=\frac{8 \times 10^8 \times 1}{2 \times 10^{11}} =4 \times 10^{-3}$

$=4 \mathrm{~mm}$

i.e. maximum elongation is $4 \mathrm{~mm}$

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