Question

At ${40}^{\circ }C$, a brass rod has a length 50 cm and a diameter 3.0 mm. It is joined 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 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. 0.28 cm
• B. 0.30 cm
• C. 0.32 cm
• D. 0.34 cm

Answer 1

The correct option is C

0.32 cm

The increase in the length of the brass rod, $\Delta l_b=2\times {10}^{-5}\times 0.5\times (240-40)=0.2cm$
The increase in the length of the steel rod, $\Delta l_s=1.2\times {10}^{-5}\times 0.5\times (240-40)=0.12cm$
$\therefore$ Increase in the length of the composite rod, $\Delta l=\Delta l_b+\Delta l_s=0.20+0.12=0.32cm$
Hence, the correct choice is (c).