Question

A metre scale made of steel reads accurately at $25^{\circ} C$ . Suppose in an experiment an accuracy of $0.06\, mm$ in $1\,m$ is required, the range of temperature in which the experiment can be performed with this metre scale is (coefficient of linear expansion of steel is $11 \times 10^{-6} /^{\circ} \, C$ )

• A. $19^{\circ} C$ to $31^{\circ} C$
• B. $25^{\circ} C$ to $32^{\circ} C$
• C. $18^{\circ} C$ to $25^{\circ} C$
• D. $18^{\circ} C$ to $32^{\circ} C$

Answer 1

Answer: (A)

$19^{\circ} C$ to $31^{\circ} C$

Answer 2

The correct answer is A:$19\degree C\space to\space 30\degree C$
Given, Coefficient of linear expansion of steel,
$\alpha=11 \times 10^{-6} /{ }^{\circ} C$
We know that,
$\Delta l=l \alpha \Delta t$
$\Rightarrow \Delta t=\frac{\Delta l}{l \alpha}$
Here, $\Delta l=6 \times 10^{-5} m \Rightarrow l=1 m$
$\Delta t=\frac{6 \times 10^{-5}}{1 \times 11 \times 10^{-6}}$
$=5.45^{\circ} C$
So, the range of temperature in which the experiment can be hence performed him this metre scale will be $19^{\circ} C$ to $31^{\circ} C$