Question

An aluminium measuring rod, which is correct at $5^{\circ }\text{C}$ measures the length of a line as $80\text{cm}$ at ${45}^{\circ }\text{C}$. If thermal coefficient of linear expansion of aluminium is $2.50\times {10}^{-5}{/}^{\circ }\text{C}$, the correct length of the line is

• A. $80.08\text{cm}$
• B. $79.92\text{cm}$
• C. $81.12\text{cm}$
• D. $79.62\text{cm}$

Answer 1

The correct option is A $80.08\text{cm}$

Given,
Length measured by aluminium rod at $5^{\circ }\text{C}$ is $80\text{cm}.....\left(1\right)$
We know from the definition of linear expansion of a material for a small change in temperature $\Delta T$
$\Delta L=L\alpha \Delta T......\left(2\right)$
From the data given in the question,
the change in temperature of the material $\left(\Delta T\right)=45-5={40}^{\circ }\text{C}$
Using this in $\left(2\right)$, we get
The increase in length
$\Delta L={\alpha }_{Al}{L}_{Al}\Delta T=(2.50\times {10}^{-5})\times 80\times 40$
$=0.08\text{cm}....\left(3\right)$
Since length of the scale increases from the calibrated length at $5{}^{\circ }\text{C}$,
The correct length of the line $L=80+0.08=80.08\text{cm}$
Hence, option (a) is the correct answer.