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  • Two rods of different materials, having coefficient of thermal expansions  and

Two rods of different materials, having coefficient of thermal expansions \alpha_1, \alpha_2 and young's moduli \gamma_1, \gamma_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 then \gamma_1:\gamma_2 is equal to

Option: 1

2: 3


Option: 2

1: 1


Option: 3

3: 2


Option: 4

4: 9


Answers (1)

best_answer

\begin{aligned} \text { strain } & =\frac{\Delta l}{l}=\frac{l \alpha \Delta \theta}{l}=\alpha \Delta \theta \\ \text { stress } & =y \times \text { strain }=y \alpha \Delta \theta \\ \text { (stress) } & =\text { (stress) } \\ y_1 \alpha_1 & =y_2 \alpha_2 \\ \frac{y_1}{y_2} & =\frac{\alpha_2}{\alpha_1}=\frac{3}{2} \end{aligned}

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Anam Khan

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