Question

A metallic tape gives correct value at ${25}^{\circ }\text{C}$. A piece of wood is being measured by this metallic tape at ${10}^{\circ }\text{C}$. The reading is $30\text{cm}$ on the tape. Then, the real length of the wooden piece must be

• A. $30\text{cm}$
• B. $>30\text{cm}$
• C. $<30\text{cm}$
• D. Data is not sufficient

Answer 1

The correct option is C $<30\text{cm}$

Given that,
Metallic tape gives correct value at ${25}^{\circ }\text{C}$.
At ${10}^{\circ }\text{C}$, the length of the metallic tape is $30\text{cm}$.
From the concept of linear expansion, we know that
Change in length of the tape with change in temperature $\Delta T$
$=\Delta L=L_0\left(\alpha \Delta T\right)$
As the temperature decreases, tape will decrease in its length.
So, the reading $30\text{cm}$ measured on the tape is lesser than the actual length of the wooden piece.
Hence, option (c) is the correct answer.