Question

‘Young’s modulus” is defined as the ratio of
A. Bulk stress and longitudinal strain
B. Hydraulic stress and hydraulic strain
C. Shearing stress and shearing strain
D. Tensile stress and longitudinal strain

Answer 1

Hint: The ratio between stress and strain is known as the modulus of elasticity. The elastic limit of the stress-strain curve has great importance in engineering designs. So the ratio between stress and strain is also considered as a property of the material.

Complete step by step answer:
The ratio between stress and strain is known as modulus of elasticity and which is found to be a characteristic of a material. The ratio of tensile or compressive stress to the longitudinal strain is known as Young’s modulus and is denoted by Y.
$Y=\dfrac{\sigma }{\varepsilon }$, where $\sigma$ is the tensile stress and $\varepsilon$ is the longitudinal strain. The unit of Young’s modulus is the same as that of the tensile stress. Since the longitudinal strain doesn’t have any units. So, the unit of Young’s modulus is $N{{m}^{-2}}$ or Pascal.
Young’s modulus will be large for the metals. These materials require a large force to make a small change in length. That’s why steel is considered as more elastic than any other metals, rubber etc. So, we can use steel for the production of heavy-duty machines and structural designs.
Therefore, the correct option is D.

Additional information:
The ratio of the shearing stress to the shearing strain is defined as the shear modulus and also known as modulus of rigidity.
$G=\dfrac{F}{A\theta }$, where F is the force, A is the area and $\theta$ is the angle of shear.
Normally, the modulus of rigidity is less than Young’s modulus.
The ratio of the hydraulic stress to the hydraulic strain is defined as the bulk modulus.
$B=\dfrac{-p}{\left( \dfrac{\Delta V}{V} \right)}$, where p is the pressure and $\left( \dfrac{\Delta V}{V} \right)$ is the change in volume.
Here, the negative sign indicates the increase in pressure decreases the volume. The bulk modulus will be positive for an equilibrium system. The reciprocal of bulk modulus is called the compressibility. The gases are more compressible compared to the solids. Therefore, bulk modulus can be defined for gases, liquids and solids.

Note: The given option represents each type of modulus. The ratio between shearing stress and shearing strain is the shear modulus. The ratio between the hydraulic stress and hydraulic strain is the bulk modulus. It is advised to learn each modulus of elasticity to choose the right option. Young’s modulus and shear modulus are only applicable for the solids and they cause the change in shape. Bulk modulus is applicable for solids, liquids, and gases and it can change the volume of the material.