Question

Which one of the following substances possess the highest elasticity?
(A) Rubber
(B) Glass
(C) Steel
(D) Copper

Answer 1

Hint: Elasticity can be defined as the property by which a material is able to stretch when it is subjected to a force and the material is able to again get back to its original shape when the given force is removed. The modulus of elasticity or elastic modulus is the measure of stiffness of the elastic material. Thus, each material has its own modulus of elasticity based on their stiffness.

Complete step by step solution
Hooke's law states that the stress is proportional to strain. The ratio of the stress to strain of an elastic substance is the elastic modulus.
Elastic modulus of rubber:
Modulus of elasticity of rubber is very low and rubber is capable of sustaining the deformation of as much as $1000\% $. After such a deformation, it forcibly and quickly retracts to its original dimensions. The rubber is resilient and yet exhibits internal damping. Modulus of elasticity of the rubber varies between $0.01\,GPa$ to $0.1\,GPa$.
Elastic modulus of glass:
Glass is perfectly an elastic material but it does not exhibit permanent deformation, until breakage. However, the glass is fragile and it will break without any warning if it is subjected to excessive stress. But the Glass is more elastic than rubber because for the given applied force per unit area, the strain which is produced in glass is much smaller than produced in rubber. Modulus of elasticity of the glass varies between $50\,GPa$ to $90\,GPa$.

Elastic modulus of steel:
The tensile tests of these steels have consistently shown that the modulus of elasticity varies with grade of steel and thickness. In relation to the elastic modulus, in the current practice for all steel grades is to assume it to be about $200\,GPa$. It is also found that the elastic modulus increases to values as high as $240\,GPa$ for the smaller thicknesses and with higher grades of steel. Thus, the Modulus of elasticity of the steel varies between $200\,GPa$ to $240\,GPa$.

Elastic modulus of copper:
Elastic region of the copper in the stress-strain curve shows highly ductile and malleable as well when the yield starts to take place then it shows plastic deformation under the applied tensile stress and once when the plastic region is completed then it starts showing brittle behavior or else becomes a material failure. Copper is tough and ductile thus it will have more elongation. Modulus of elasticity of copper is $117\,GPa$.

Thus, the steel possesses the highest elasticity among the given materials.

Hence the option (C) is correct.

Note: There are different types of stresses and their corresponding strains within the elastic limit are related which are referred to as elastic constants. Types of elastic constants are:
(i) Modulus of elasticity or Young’s modulus and it is denoted by $\left( E \right)$,
(ii) Bulk modulus and it is denoted by $\left( K \right)$ and
(iii) Modulus of rigidity or shear modulus and it is denoted by $\left( {M,\,C,\,G} \right)$.