Question

A steel scale measures the length of a copper rod as L cm when both are at ${20}^{\circ }C$, the calibration temperature for the scale. If the coefficients of linear expansion for steel and copper are ${\alpha }_s$ and ${\alpha }_c$ respectively, what would be the scale reading (in cm) when both are at ${21}^{\circ }C$?

• A. $\frac{L(1+{\alpha }_c)}{(1+{\alpha }_s)}$
• B. $L\frac{{\alpha }_c}{{\alpha }_s}$
• C. $L\frac{{\alpha }_s}{{\alpha }_c}$
• D. $L$

Answer 1

The correct option is A

$\frac{L(1+{\alpha }_c)}{(1+{\alpha }_s)}$

The length of 1 cm division of the steel scale at ${21}^{\circ }C$ is $1cm\times [1+{\alpha }_s(21-20\left)\right]=(1+{\alpha }_s)cm$
The length of cooper rod at ${21}^{\circ }C$ will be $Lcm\times [1+{\alpha }_c(21-20\left)\right]=L(1+{\alpha }_c)cm$
$\therefore$ Scale reading at ${21}^{\circ }C=\frac{L(1+{\alpha }_c)}{(1+{\alpha }_s)}$
Hence, the correct choice is (a).