Question

An aluminium measuring tape which is correct at 10${}^o$ C measures the length of a line as 80 cm at 50${}^o$. If thermal coefficient of linear expansion of aluminium is of 2.50 x 10${}^{-5}$ per${}^o$ C,the correct length of the line is

• A. 79.92 cm
• B. 79.68 cm
• C. 80.08 cm
• D. 80.32 cm

Answer 1

Answer: (C)

80.08 cm

Let the number of unit lengths originally at ${10}^{\circ }C$ that add upto the lenght of the line be $x$ and that at ${50}^{\circ }C$ be $y$.

Hence the length of the line can be expressed as

$L=x{d}_1=y{d}_2$

where $d_1,d_2$ are the unit lengths.

Due to thermal expansion, $d_2=d_1(1+\alpha \Delta \theta )$

$⟹x=y(1+\alpha \Delta \theta )$

Thus the length as measured by tape at ${10}^{\circ }C=\frac{80\times x}{y}$$=80.08cm$