Question

The scale on a steel meter stick is calibrated at ${15}^{\circ }\text{C}$. Find the error in the reading of $60\text{cm}$ at ${27}^{\circ }\text{C}$. Given ${\alpha }_{\text{steel}}=1.2\times {10}^{-5}{}^{\circ }{\text{C}}^{-1}$

• A. $0.864\text{cm}$
• B. $0.0864\text{cm}$
• C. $0.00864\text{cm}$
• D. $8.64\text{cm}$

Answer 1

The correct option is C $0.00864\text{cm}$

We know that,
At high temperatures, actual reading is more than the scale reading. To find the error in the reading, we will use the formula
$\alpha =\left(\frac{1}{L}\right)\left(\frac{\Delta L}{\Delta T}\right)$
Then, error in reading $=\Delta L$
$=\text{scale reading}\left(L\right)\times \alpha \times \Delta T$
$=\left(60\right)(1.2\times {10}^{-5})({27}^{\circ }\text{C}-{15}^{\circ }\text{C})$
$=0.00864\text{cm}$