Determine the pressure required at the ends of a steel wire (length 10text cm ) to maintain a constant length when the temperature is increased by 100^ circ text C . (Given: Steel Young's modulus Y = 2 times 10^ 11 text Nm ^ -2 and coefficient of thermal expansion alpha = 1.1 times 10^ -5 text K ^ -1 )

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EEJ MAIN Physics QUESTION #7079

Question 1

Determine the pressure required at the ends of a steel wire (length $10\text{ cm}$) to maintain a constant length when the temperature is increased by $100^{\circ}\text{C}$. (Given: Steel Young's modulus $Y = 2 \times 10^{11}\text{ Nm}^{-2}$ and coefficient of thermal expansion $\alpha = 1.1 \times 10^{-5}\text{ K}^{-1}$)

$2.2 \times 10^{7}\text{ Pa}$
$2.2 \times 10^{6}\text{ Pa}$
$2.2 \times 10^{8}\text{ Pa}$✔️
$2.2 \times 10^{9}\text{ Pa}$

Correct Answer Explanation

The thermal stress required to keep the length constant is given by the formula:

$\text{Stress} = Y \alpha \Delta T$
Substituting the values: $\text{Stress} = (2 \times 10^{11}) \times (1.1 \times 10^{-5}) \times 100$
$\text{Stress} = 2.2 \times 10^{8}\text{ Pa}$

Pressure is equivalent to the stress applied at the ends.

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