Question

A steel metre scale is to be ruled so that the millimetre intervals are accurate within about $5\times {10}^{-5}mm$ at a certain temperature. The maximum temperature variation allowable during the ruling of the millimetre marks is ($\alpha$ for steel $=11\times {10}^{-6}{}^o{C}^{-1}$)

• A. $8^{o}C$
• B. $9^{o}C$
• C. ${4.5}^{o}C$
• D. ${10}^{o}C$

Answer 1

The correct option is C ${4.5}^{o}C$

Use formula of thermal expansion ,

$\Delta L=L_0\alpha \Delta T$

where $\Delta L$ is the change in length of object after changing temperature

$L_0$ is the initial length of object

$\Delta T$ is the temperature change

and $\alpha$ is the coefficient of linear expansion

Here, $\Delta L=5\times {10}^{-5}mm=5\times {10}^{-8}m$

$L_0=1mm={10}^{-3}m$

$\alpha =11\times {10}^{-6}{C}^{-1}$

Now, from formula,

$5\times {10}^{-8}={10}^{-3}\times 11\times {10}^{-6}\times \Delta T$

$\Delta T=\frac{50}{11}$

$\Delta T=4.5C^{-1}$

Option C is correct.