Question

Two rods identical in geometry but of different materials having coefficient of thermal expansion ${\alpha }_{1}and{\alpha }_2$ and Youngs moduli $Y_{1}and{Y}_2$ respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of the rods If ${\alpha }_1:{\alpha }_2$ = 2 : 6, the thermal stresses developed in the two rods are equal provided $Y_1:Y_2$ is equal to

• A. 2 : 3
• B. 1 : 1
• C. 3 : 1
• D. 4 : 9

Answer 1

The correct option is C 3 : 1

$△l=l\alpha △T\Rightarrow △l/l=\alpha △T$

stress = YX strain

stress = $Y\alpha △T$

For first rod, stress=$Y_1{\alpha }_1△T$

For second rod, stress=$Y_2{\alpha }_2△T$

Since, stress are equal

$\therefore Y_1{\alpha }_1△T=Y_2{\alpha }_2△T$

or $Y_1/Y_2={\alpha }_2/{\alpha }_1$

$=\frac{6}{2}=\frac{3}{1}$

$Y_1:Y_2=3:1$