Question

Which one is more elastic, steel or rubber? Explain.

Answer 1

Hint: Contrary to our intuitive understanding of elasticity where we only think of how easily a body deforms under an applied deforming force, try and account for the reformation of the body after the deforming force is removed. In other words, think in terms of how steel requires more deforming force to produce the same strain as in rubber and what it means in terms of elasticity.

Formula used:
Modulus of elasticity $M= \dfrac{stress}{strain}$ where stress = $\dfrac{Force}{Area}$ and strain = $\dfrac{change\; in\; dimensions}{original\; dimensions}$, where the dimensions may be length, area or volume.

Complete answer:
Let us first define and understand what elasticity means from a physics standpoint.
Elasticity is the ability of a body to resist a deforming force and return to its original form when that influencing force is removed. It is the ratio of stress and strain, where stress is the deforming force experienced by an object whereas strain is the change in the shape of an object when the deforming force or stress is applied. This ratio is also known as the modulus of elasticity.

The higher the modulus of elasticity the more resistive the body is to the deforming force. This means that more stress is needed to create a said amount of strain in this object relative to other objects. Thus, if a body A is more resistive to the deforming force than another body B in bringing out the same amount of strain in both, we say that body A is more elastic than body B.

Modulus of elasticity $M= \dfrac{stress}{strain}$

Now that we understand what elasticity is, what stress and strain are and how they are related to each other let us look at this in the context of our question.

So, let us consider steel and rubber.

Assume you have two wires, one made of steel, and one made of rubber and they are both of the same length and cross-sectional area. Now, suppose you want to extend both the wires by say $2\;cm$. Which wire do you think gets stretched easily, and which wire do you think resists to stretching as easily as the other?

If you thought rubber and steel respectively, then you are absolutely right.

Therefore, we have the steel wire being more resistive to the pulling force and from our definition since we have to apply more force to bring out the same strain of $2\;cm$ in the steel wire in comparison to the rubber wire we say that steel is more elastic than rubber.

Note:
It is a common misconception to say that just because the rubber stretches more easily than steel, rubber is more elastic. This is because elasticity does not necessarily mean how easily a body deforms but it is also how easily the body reforms back to its original shape. The greater the resistance to deformation, the greater is its elasticity and the faster it returns back to its original form when the deforming force is removed because it basically reforms back with a rate proportional to the deformation force applied. Therefore, steel comes back to its original shape faster than rubber and hence steel is more elastic than rubber.