Question

A brass rod of length 500 mm and diameter 3 mm is joined to a steel rod of same length and diameter at $\text{50}{}^{\text{o}}\text{C}\text{.}$ If the coefficients of linear expansion of brass and steel are $2.5\times {10}^{-5}{}^o{C}^{-1}$ and $1.25\times {10}^{-5}{}^o{C}^{-1},$ then change in length of the combined rod at $200{}^{o}C$ is :

• A. 2.4 mm
• B. 2.8 mm
• C. 3.2 mm
• D. 3.6 mm

Answer 1

Answer: (B)

Change in length of brass rod $\Delta l_B={\alpha }_B{l}_B(T_2-T_1)$ $=2.5\times {10}^{-5}\times 500\times (200-50)$ $=1.875mm$ Similarly change in length of steel rod $\Delta l_S={\alpha }_S{l}_S(T_2-T_1)$ $=1.25\times {10}^{-5}\times 500\times (200-50)$ $=0.9375mm$ Therefore, change in length of the combined rod $=\Delta l_B+l_S=1.875+0.9375$ $=2.8125mm=2.8mm$