Question

A scale which is calibrated at ${10}^{\circ }\text{C}$ measures the length of a stick to be $60\text{cm}$, at temperature ${30}^{\circ }\text{C}$ . If thermal coefficient of linear expansion of the rod is $2\times {10}^{-5}{/}^{\circ }\text{C}$, the correct length of the stick in $\text{cm}$ is:

• A. $60.015$
• B. $60.024$
• C. $60.400$
• D. $60.600$

Answer 1

The correct option is B $60.024$

When measuring at high temperature, the scale will be more than its calibrated length. So, actual length of stick will be more that measured length.
Change in length $\Delta l=l\alpha \Delta T$
$=60\times 2\times {10}^{-5}\times (30-10)$
$=0.024\text{cm}$
So, correct length $=l+\Delta l=60+0.024$
$=60.024\text{cm}$