Question

Why is the modulus of elasticity of steel is greater than that of rubber under the same stress?

Answer 1

Step 1: Given data

Given, stress is the same for both rubber and steel

We know,

Step 2: Formula used and conclusion

$Modulusofelasticity=\frac{stress}{strain}$

Let modulus of elasticity be denoted by Y

Then, $Y=\frac{stress}{strain}$

Since it is given that stress is same for rubber and steel, we can write,

$Y\propto \frac{1}{strain}(stressiscons\tan t)$

i.e., the modulus of elasticity is inversely proportional to strain.

$\because$We know

$$\begin{gathered} Strain=\frac{∆l}{l} \\ \therefore Y\propto \frac{l}{∆l} \end{gathered}$$

for the same length, since rubber is more elastic, extension,$∆l$ is more for rubber as compared to steel.

We know that rubber is more flexible than steel and will undergo a huge change in length as compared to steel.

Therefore, since $Y\propto \frac{1}{∆l}$, modulus of elasticity is more for steel.

The modulus of elasticity of steel is greater than that of rubber under the same stress because, the modulus of elasticity is inversely proportional to strain