Question

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

• A. $80.08cm$
• B. $79.92cm$
• C. $81.12cm$
• D. $79.62cm$

Answer 1

The correct option is A $80.08cm$

The percentage error in the measurement is given as,

$e\%=\left(\frac{1+45\alpha }{1+5\alpha }-1\right)\times 100$

$e\%=\left(\frac{1+45\times 2.5\times {10}^{-5}}{1+5\times 2.5\times {10}^{-5}}-1\right)\times 100$

$e\%=0.1\%$

The correct length of the line is given as,

$l=80+\left(80\times 0.1\%\right)$

$l=80.08cm$