Question

Two rods, one of aluminium and the other made of steel, having initial length ${\ell }_1$ and ${\ell }_2$ are connected together to form a single rod of length ${\ell }_1+{\ell }_2$. The coefficient of linear expansion for aluminium and steel are ${\alpha }_a$ and ${\alpha }_s$ respectively. If the length of each rod of increases by the same amount when their temperature are raised by $t^{o}C$ then find the ratio $\frac{{\ell }_1}{{\ell }_1+{\ell }_2}$

• A. $\frac{{\alpha }_s}{{\alpha }_a}$
• B. $\frac{{\alpha }_a}{{\alpha }_s}$
• C. $\frac{{\alpha }_s}{{(\alpha }_a+{\alpha }_s)}$
• D. $\frac{{\alpha }_a}{{(\alpha }_a+{\alpha }_s)}$

Answer 1

Answer: (C)

$\frac{{\alpha }_s}{{(\alpha }_a+{\alpha }_s)}$

$l_1{\alpha }_{a}t=l_1{\alpha }_a$

$\frac{l_2}{l_1}=\frac{{\alpha }_a}{{\alpha }_s}$

$\frac{l_2+l_1}{l_1}=\frac{{\alpha }_0+{\alpha }_s}{{\alpha }_s}$

Option C is correct.