Question

The length, coefficient of thermal expansion and Young's modulus of bar A are twice that of bar B. If the temperature of both bars is increased by the same amount while preventing any expansion, then the ratio of stress developed in bar A to that in bar B will be

• A. $2$
• B. $4$
• C. $8$
• D. $16$

Answer 1

The correct option is B $4$

Temperature Stress $=E\propto \Delta T$
$\frac{\text{Stress in bar A}}{\text{Stress in bar B}}=\left(\frac{E_A}{E_B}\right)\left(\frac{{\alpha }_A}{{\alpha }_B}\right)=2\times 2=4$