Question

The ratio of shear stress to shear strain is ______.
A. Poisson’s ratio
B. Young’s modulus
C. Bulk modulus
D. Rigidity modulus

Answer 1

Hint: For this question we will be discussing what is the ratio of shear stress to shear strain. We know that Shear modulus or modulus of rigidity gives the relation between shear stress and shear strain. We will be discussing more about shear modulus for this question.

Complete step by step answer:
Shear stress is the force that causes deformation of material along a plane which is parallel to applied shear stress. Shearing is the act of removing material from the surface of a body by applying stress. Shear stress occurs when the force is applied parallel to a surface. Such a force is called a shear force. Now, we know that strain is defined as the change in dimension such as length to original dimension of the body. Shear strain is the change occurring in the dimension due to shear stress. Shear stress is given by force over area. While, shear strain is given by change in length over original length $${\displaystyle \frac{\mathrm{\Delta }x}{x}}$$.
Shear modulus or modulus of rigidity is used to measure the rigidity of a body. The ratio of shear stress over shear strain is known as Shear modulus. It is denoted by G. The SI unit of rigidity modulus is Pascal (Pa).
So, we know the correct answer is option D.

Note:
Young’s modulus is the ratio of tensile stress by tensile strain. It is denoted by E as it is also known as modulus of elasticity. While Bulk modulus is the ratio of volumetric stress to volumetric strain. It is denoted by K. The relation between Bulk modulus, Young’s modulus and shear modulus is given by the formula
$$E={\displaystyle \frac{9KG}{G+3K}}$$.