Question

A metre scale is made up of steel and measures correct length at ${16}^{o}C$ . What will be the percentage error if this scale is used
(a) on a summer day when the temperature is ${46}^{o}C$ and
(b) on a winter day when the temperature is $6^{o}C?$
Coefficient of linear expansion of steel $=11\times {10}^{-6}$${}^o{C}^{-1}$

Answer 1

(a)

The change in length is given as,

$\Delta L=L\alpha \Delta T$

$\frac{\Delta L}{L}=11\times {10}^{-6}\times 30$

The error percentage is given as,

$\%e=\left(\frac{\Delta L}{L}\times 100\right)\%$

$\%e=\left(11\times {10}^{-6}\times 30\times 100\right)\%$

$=3.3\times {10}^{-2}\%$

(b)

The change in length is given as,

$\Delta L=L\alpha \Delta T$

$\frac{\Delta L}{L}=11\times {10}^{-6}\times 10$

The error percentage is given as,

$\%e=\left(\frac{\Delta L}{L}\times 100\right)\%$

$\%e=\left(11\times {10}^{-6}\times 10\times 100\right)\%$

$=1.1\times {10}^{-2}\%$

Thus, the error percentages are $3.3\times {10}^{-2}\%$ and $1.1\times {10}^{-2}\%$.