Question

At ${20}^{\circ }C$ a steel ruler of 20 cm long is graduated to give correct reading but when it is used at a temperature of ${40}^{\circ }C$ what will be the actual length of the steel ruler ? $[{\alpha }_{\text{steel}}=1.2\times {10}^{-3}{\left({}^{0}C\right)}^{-1})$

• A. 22.02 cm
• B. 19.6 cm
• C. 20.0048 cm
• D. 18.0002 cm

Answer 1

The correct option is C 20.0048 cm

Given:

The initial temperature of the steel ruler is ${20}^{\circ }C$

The final temperature of steel ruler is ${40}^{\circ }C$

The length of the steel ruler is $20cm$

The coefficient of expansion of the ruler is $1.2\times {10}^{-3}{/}^{\circ }C$

The change in the length of the steel ruler due to change in temperature is given by:

$L=L_o(1+\alpha \Delta T)$

Substitute the values:

$L=20[1+1.2\times {10}^{-3}\times (40-20\left)\right]$

$L=20.0048cm$