1. Tardigrade
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  3. Physics
  4. A steel wire of length 20 cm and uniform cross-section 1 mm 2 is tied rigidly at both the ends. The temperature of the wire is altered from 40° C to 20° C. Coefficient of linear expansion of steel is α=1.1 × 10-5 ° C -1 and Y for steel is 2.0 × 1011 Nm 2 the tension in the wire is

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Q. A steel wire of length $20 \,cm$ and uniform cross-section $1 \,mm ^{2}$ is tied rigidly at both the ends. The temperature of the wire is altered from $40^{\circ} C$ to $20^{\circ} C$. Coefficient of linear expansion of steel is $\alpha=1.1 \times 10^{-5}{ }^{\circ} C ^{-1}$ and $Y$ for steel is $2.0 \times 10^{11} Nm ^{2}$ the tension in the wire is

Mechanical Properties of Solids

Solution:

Increase in length due to rise in temperature $\Delta L=\alpha L \Delta T$
As, $Y=\frac{F L}{A \Delta L}$
So, $F=\frac{Y A \Delta L}{L}=\frac{Y A \times \alpha L \Delta T}{L}=Y A \alpha \Delta T$
$\therefore F=2 \times 10^{11} \times 10^{-6} \times 1.1 \times 10^{-5} \times 20=44 N$