Question

The stress that has to be applied to the ends of a steel wire of length 20 cm to keep its length constant, when its temperature is raised by \(100^\circ C\) is \(2.2 \times 10^x \, \text{Pa}\). The value of \(x\) is
(Given \( Y = 2 \times 10^{11} \, \text{Nm}^{-2}, \, \alpha = 1.1 \times 10^{-5} \, ^\circ C^{-1} \))

Hint:

If expansion is restricted, directly use: Stress = \( Y \alpha \Delta T \).

Answer 1

Concept: Thermal stress when expansion is prevented: \[ \text{Stress} = Y \alpha \Delta T \]

Step 1: Substitute values.
\[ \text{Stress} = (2 \times 10^{11})(1.1 \times 10^{-5})(100) \]

Step 2: Simplify.
\[ = 2 \times 1.1 \times 100 \times 10^{11-5} = 2.2 \times 100 \times 10^6 = 2.2 \times 10^8 \, \text{Pa} \]

Step 3: Compare with given form.
\[ 2.2 \times 10^x \Rightarrow x = 8 \]