Question

A steel scale measuresthe length of a copper wire as 80.0 cm when both are at ${20}^{\circ }C$ (the calibration temperature for scale). What would be the scale read for the length of the wire when both are at 40C ? $(Given{\alpha }_{steel}=11\times 10-6pe{r}^{0}Cand{\alpha }_{copper}=17\times {10}^{-6}per{}^{0}C)$

• A. 80.0096 cm
• B. 80.0272 cm
• C. 1 cm
• D. 25.2 cm

Answer 1

The correct option is A

80.0096 cm

With temperature rise (same ${25}^{\circ }C$ for both), steel scale and copper wire both expand. Hence length of copper wire w.r.t. steel scale or apparent length of copper wire after rise in temperature

$L_{app}=L_{cu}^{\prime }-L_{steel}^{\prime }=\left(L_0\right(1+{\alpha }_{cu}△\theta )-L_0(1+{\alpha }_{steel}△\theta )$

$\Rightarrow L_{app}=L_0({\alpha }_{cu}-{\alpha }_{steel})△\theta$

$=80(17\times {10}^{-6}-11\times {10}^{-6})\times 20=80.0096cm$