Question

An aluminium rod (length $l_1$ and coefficient of linear expansion ${\alpha }_A$) and a steel rod (length $l_2$ and coefficient of linear expansion ${\alpha }_B$) are joined together. If the length of each rod increased by the same amount when their temperatures are raised by $t^{o}C$, then $l_1/(l_1+l_2)$ is:

• A. ${\alpha }_A/{\alpha }_B$
• B. ${\alpha }_B/{\alpha }_A$
• C. ${\alpha }_B/{\alpha }_A+{\alpha }_B$
• D. ${\alpha }_A/{\alpha }_A+{\alpha }_B$

Answer 1

The correct option is C ${\alpha }_B/{\alpha }_A+{\alpha }_B$

An aluminium rod (length l1 and coefficient of linear expansion αA) and a steel rod (length l2 and coefficient of linear expansion αB) are joined together. If the length of each rod increased by the same amount when their temperatures are raised by toC, then $\frac{l_1}{(l_1+l_2)}$ is

If amount of heat is same the lenght is also increase by same amount hence

$l_1{\alpha }_1=l_2{\alpha }_2$

$\frac{l_2}{l_1}=\frac{{\alpha }_1}{{\alpha }_2}$

$\frac{l_2}{l_1}+1=\frac{{\alpha }_1}{{\alpha }_2}+1$

$\frac{l_2+l_1}{l_1}=\frac{{\alpha }_1+{\alpha }_2}{{\alpha }_2}$

$\frac{l_1}{(l_1+l_2)}=$$\frac{{\alpha }_2}{({\alpha }_1+{\alpha }_2)}$