Question

The pressure that has to be applied to the ends of a steel wire of length $10 \,cm$ to keep its length constant when its temperature is raised by $100^\circ \,C$ is :
(For steel Young's modulus is $2 \times 10^{11} Nm^{-2}$ and coefficient of thermal expansion is $1.1 \times 10^{-5}\, K^{-1}$)

• A. $2.2 \times 10^8\, Pa$
• B. $2.2 \times 10^9\, Pa$
• C. $2.2 \times 10^7 \,Pa$
• D. $2.2 \times 10^6\, Pa$

Answer 1

Answer: (A)

As length is constant,
Strain $=\frac{\Delta L}{L}=\alpha \,\Delta Q $
Now pressure=stress $=\Upsilon \times $ strain
$=2 \times 10^{11} \times 1.1 \times 10^{-5} \times 100 $
$=2.2 \times 10^{8}\, Pa$