Question

If the temperature of a wire of length $2 \,m$ and area of cross-section $1 \,cm ^{2}$ is increased from $0^{\circ} C$ to $80^{\circ} C$ and is not allowed to increase in length, then force required for it is $\left\{Y=10^{10} N / m ^{2}, \alpha=10^{-6} /{ }^{\circ} C \right\}$

• A. 80 N
• B. 160 N
• C. 400 N
• D. 120 N

Answer 1

Answer: (A)

Thermal expansion would be $=L \propto \Delta T$
Where $L=$ original length
$\alpha=$ coefficient of linear expansion
$\Delta T=$ Change in temperature
So substituting values
$\Delta L=2 \times 10^{-6} \times 80$
$\Delta L=1.6 \times 10^{-4} m$
Now $\Delta L=\frac{F L}{A Y}$
$\frac{\Delta L \times A Y}{L}=F$
Substitute values
$\frac{1.6 \times 10^{-4} \times 10^{10} \times 1}{2 \times 10000}=F$
$80 \,N =F$