Question

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

• A. 2
• B. 4
• C. 8
• D. 16

Answer 1

The correct option is B 4

Bar A Bar B

$l_A=2l$ $l_A=2l$

${\alpha }_A=2\alpha$ ${\alpha }_B=\alpha$

$E_A=2E$ $E_B=E$

Thermal stress developed due to prevention of expansion is ${\sigma }_{Th}=E\alpha t$

$\therefore \frac{({\sigma }_{Th}{)}_A}{({\sigma }_{Th}{)}_B}=\frac{(E\alpha t{)}_A}{(E\alpha t{)}_B}=\frac{\left(2E\right)\left(2\alpha \right)t}{E\alpha t}=\frac{4}{1}$