Question

A steel rod of diameter $1\text{cm}$ is clamped firmly at each end, when its temperature is ${25}^{\circ }C$, so that it cannot contract on cooling. The tension in the rod, at $0^{\circ }C$ is approximately, $(\alpha ={10}^{-5}{/}^{\circ }\text{C},Y=2\times {10}^{11}{\text{Nm}}^{-2})$

• A. $4000\text{N}$
• B. $7000\text{N}$
• C. $7400\text{N}$
• D. $4700\text{N}$

Answer 1

The correct option is A $4000\text{N}$

The tensile stress in the rod, due to change in temperature is,
Stress$=Y\alpha \left(\Delta T\right)$
And, the force is given by, $F=\text{(Stress)}\times A$
$\therefore F=AY\alpha \left(\Delta T\right)$
$=\pi \times (5\times {10}^{-3}{)}^2\times 2\times {10}^{11}\times {10}^{-5}\times 25$

$F\approx 4000\text{N}$

Hence, $\left(A\right)$ is the correct answer.