Question
Explain why steel is more elastic than rubber.
✓
Answer
Consider two pieces of wires, one of steel and the other of rubber.
Suppose both are of equal length (L) and of equal area of cross-section (a).
Let each be stretched by equal forces, each being equal to F.
We find that the change in length of the rubber wire (l_r) is more than that of the steel
$(l_s) i.e. l_r < ls.$ If $Y_s$_ and $Y_r$_ the Young's moduli of steel and rubber respectively,
then from the definition of Young's modulus, $\text{Y}_\text{s}=\frac{\text{F.L}}{\text{a.l}_\text{s}}\text{ and }\text{Y}_\text{r}=\frac{\text{F.L}}{\text{a.l}_\text{r}}$
$\therefore\frac{\text{Y}_\text{s}}{\text{Y}_\text{r}}=\frac{\text{l}_\text{r}}{\text{l}_\text{s}}.$
As $\text{l}_\text{r}>\text{l}_\text{s}\therefore\frac{\text{Y}_\text{s}}{\text{Y}_r}>1\ \text{or }\text{Y}_\text{r}$
i.e., the Young's modulus of steel is more than that of rubber.
Hence steel is more elastic than rubber.OR
Any material which offers more opposition to the deforming force to change its configuration is more elastic.
Suppose both are of equal length (L) and of equal area of cross-section (a).
Let each be stretched by equal forces, each being equal to F.
We find that the change in length of the rubber wire (l_r) is more than that of the steel
$(l_s) i.e. l_r < ls.$ If $Y_s$_ and $Y_r$_ the Young's moduli of steel and rubber respectively,
then from the definition of Young's modulus, $\text{Y}_\text{s}=\frac{\text{F.L}}{\text{a.l}_\text{s}}\text{ and }\text{Y}_\text{r}=\frac{\text{F.L}}{\text{a.l}_\text{r}}$
$\therefore\frac{\text{Y}_\text{s}}{\text{Y}_\text{r}}=\frac{\text{l}_\text{r}}{\text{l}_\text{s}}.$
As $\text{l}_\text{r}>\text{l}_\text{s}\therefore\frac{\text{Y}_\text{s}}{\text{Y}_r}>1\ \text{or }\text{Y}_\text{r}$
i.e., the Young's modulus of steel is more than that of rubber.
Hence steel is more elastic than rubber.OR
Any material which offers more opposition to the deforming force to change its configuration is more elastic.
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