Question

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

• 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 ${25}^{o}C$ 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
$L_{app}=L_{Cu}-L_{steel}=\left[L_0\right(1+{\alpha }_{Cu}△\theta )-L_0(1+{\alpha }_s+△\theta \left)\right]$
$\Rightarrow L_{app}=L_0({\alpha }_{Cu}-{\alpha }_s)△\theta$
=$80(17\times {10}^{-6}-11\times {10}^{-6})\times 20=80.0096cm$