Question

Two metal rods of same length and same area of cross section are fixed, end to end between rigid supports. Young's modulus of elasticity of two metal rods are $Y_{1}and{Y}_2$, and coefficient of linear expansion are ${\alpha }_{l}and{\alpha }_2$. When the rods are cooled the junction does not change its position, if

• A. $\frac{Y_1}{Y_2}=\sqrt{\frac{{\alpha }_1}{{\alpha }_2}}$
• B. $\frac{Y_1}{Y_2}=\frac{{\alpha }_1}{{\alpha }_2}$
• C. $\frac{Y_1}{Y_2}=\frac{{\alpha }_2^2}{{\alpha }_1^2}$
• D. $Y_{1\alpha 1}=Y_{2\alpha 2}$

Answer 1

The correct option is D $Y_{1\alpha 1}=Y_{2\alpha 2}$

$Y_{1\alpha 1}\Delta T=Y_{2\alpha 2}\Delta T$

$Y_{1\alpha 1}=Y_{2\alpha 2}$