Question

A steel wire of length $20 cm$ and uniform cross section $1\, mm ^{2}$ is tied rigidly at both the ends. If temperature of the wire is altered from $40^{\circ} C$ to $20^{\circ} C$. Calculate the change in tension. (Given coefficient of linear expansion of steel $\alpha=1.1 \times 10^{-5} /{ }^{\circ} C$ and Young's modulus $Y$ for steel $=2 \times 10^{11} N / m ^{2}$ )

• A. 88 N
• B. 11 N
• C. 44 N
• D. 22 N

Answer 1

Answer: (C)

The change in tension, when wire is cooled is given by
$F=y A \alpha \Delta \theta $
Given, $ \Delta \theta=40^{\circ}-20^{\circ}=20^{\circ} C $,
$A=1 \,mm ^{2}=1 \times 10^{-6} m ^{2}, $
$\alpha=1.1 \times 10^{-5} /{ }^{\circ} C , $
$Y=2 \times 10^{11} N / m ^{2} $
$\therefore F=2 \times 10^{11} \times 10^{-6} \times 1.1 \times 10^{-5} \times 20$
$\Rightarrow F=44 \,N$