Question

A $20\text{cm}$ long steel ruler is graduated to give correct measurement at $20{}^{\circ }\text{C}$. What will be the actual length of the ruler in the desert at $40{}^{\circ }\text{C}$ ?
$[\alpha =1.2\times {10}^{-5}/{}^{\circ }\text{C}]$

• A. $20.0032\text{cm}$
• B. $20.0016\text{cm}$
• C. $20.0048\text{cm}$
• D. $20.0008\text{cm}$

Answer 1

The correct option is C $20.0048\text{cm}$

Given:
Length of rod at $20{}^{\circ }\text{C}=20\text{cm}$
Co-efficient of linear expansion, $\alpha =1.2\times {10}^{-5}/{}^{\circ }\text{C}$
To find: Length of rod at $40{}^{\circ }\text{C}$
We know, length of the rod at any temperature $T$ is given by
$L=L_0[1+\alpha (T-T_0\left)\right]$
$=20[1+1.2\times {10}^{-5}({40}^{\circ }\text{C}-{20}^{\circ }\text{C}\left)\right]$
$=20.0048\text{cm}$