Two rods of different materials having coefficient of thermal exp… - Vidyadip

MCQ

Two rods of different materials having coefficient of thermal expansion $\alpha_1,\alpha_2$ and Young's modulus $Y_1, Y_2$, 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 $\alpha_1:\alpha_2=2:3,$ the thermal stresses developed in the two rods are equal provided $Y_1 : Y_2$ is equal to:

A
$2 : 3$
B
$1 : 1$
✓
$3 : 2$
D
$4 : 9$

✓

Answer

Correct option: C.

$3 : 2$

Expansion in rod due to rise in temperature $=$ compression in rod,
$\therefore\frac{\alpha_1}{\alpha_2}=\frac{\text{Y}_1}{\text{Y}_2}$ or $\frac{\alpha_2}{\alpha_1}=\frac{3}{2}$

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