Question

Young's modulus and shear modulus can be defined only in

• A. solids and liquids
• B. liquids
• C. gases
• D. gases and liquids
• E. solids

Hint:

Fluids have bulk modulus (resistance to compression), but not Young's or shear modulus.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
This question is about the mechanical properties of different states of matter. Moduli of elasticity describe a material's resistance to deformation. We need to identify which states of matter can resist the types of deformation associated with Young's modulus and shear modulus.
Step 2: Detailed Explanation:
Let's define the moduli:
Young's Modulus (Y): It is the ratio of longitudinal stress to longitudinal strain. It measures a material's resistance to a change in length when stretched or compressed. For a material to have a well-defined length, it must have a definite shape.
Shear Modulus (G) or Modulus of Rigidity: It is the ratio of shearing stress to shearing strain. It measures a material's resistance to a change in shape (a deformation where parallel planes slide past one another).
Now let's consider the states of matter:
Solids: Solids have a definite shape and volume. They resist changes in both length and shape. Therefore, Young's modulus and shear modulus are well-defined for solids.
Liquids and Gases (Fluids): Fluids do not have a definite shape. They take the shape of their container. They cannot sustain a shearing stress; they will simply flow. Because they do not resist a change in shape, their shear modulus is effectively zero. Similarly, because they do not have a fixed initial length, Young's modulus is not a meaningful concept for fluids. Fluids do, however, resist changes in volume, so they have a Bulk Modulus.
Therefore, both Young's modulus and shear modulus are properties that are only defined for solids.
Step 3: Final Answer:
Young's modulus and shear modulus can be defined only in solids. This corresponds to option (E).