Question

At ${40}^{\circ }C$, a brass rod has a length $50\text{cm}$ and a diameter $3.0\text{mm}$, is joined in series to a steel rod of the same length and diameter at the same temperature. What is the change in the length of the composite rod(in $\text{cm}$), when it is heated to ${240}^{\circ }C$ ?
The coefficients of linear expansion of brass and steel are $2.0\times {10}^{-5}{}^{\circ }{C}^{-1}$ and $1.2\times {10}^{-5}{}^{\circ }{C}^{-1}$ respectively:

• A. 0.32
• B. 0.320

Answer 1

Answer: (A), (B)

Change in length of composite rod
$=\Delta l_b+\Delta l_s$
$=l_b{\alpha }_b\Delta T+{\alpha }_s{l}_s\Delta T$
$=[50\times {10}^{-2}\times 2\times {10}^{-5}\times 200]+[50\times {10}^{-2}\times 1.2\times {10}^{-5}\times 200]$
$={10}^4\times {10}^{-7}\times 3.2$
$=3.2\times {10}^{-3}$m
$=0.32$ cm