Question

A metal rod has the length of $50cm$ at ${20}^{\circ }C$. When it is heated to ${95}^{\circ }C$, its length becomes $50.06cm$. Find the length of the rod at $0^{\circ }C$.

Answer 1

Length for rod at ${20}^o$ is 50cm.

When temperature changes to ${95}^{o}C$, length is 50.06 cm.

$\Delta L=50.06-50=0.06cm$

and $\Delta T=95-20={75}^{o}C$

So change is length $\Delta L=L_{20}\times \alpha \Delta T=50\times \alpha \times 75$

$0.06=50\times \alpha \times 75$ .....(1)

Let the change in length of rod when temperature changes from 20 to 0 be $\Delta L_1$ and $\Delta T=0-20=-20$

So $\Delta L_1=50\times \alpha \times (-20)$ ....(2)

From (1) and (2), we get $\Delta L_1=-0.02$

Length at $0^o$ is $50-0.02=49.98cm$