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 $Y_1\text{and}{Y}_2$, and coefficient of linear expansion are ${\alpha }_1\text{and}{\alpha }_2$. When the rods are cooled the junction does not change its position, if

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

Answer 1

The correct option is D $Y_1{\alpha }_1=Y_2{\alpha }_2$

$Y_1{\alpha }_1\Delta T=Y_2{\alpha }_2\Delta T$

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