Shearing stress occurs when tangential forces are applied to a body, causing layers to slide over one another and changing the shape (angles) of the object while the volume remains constant. Tensile and compressive stresses involve changes in length, while bulk stress involves changes in volume.

Young's modulus measures a material's stiffness; a higher value means the material requires more stress to produce a given strain, which is the definition of being more elastic in physics. Steel has a higher Young's modulus than copper, meaning it returns to its original shape more effectively under stress, making it more elastic in the technical sense of the term.

Elongation (ΔL) is given by ΔL = (FL) / (AY), where A = πr². Elongation is directly proportional to length (L) and inversely proportional to the square of the diameter (d²). Comparing the ratios L/d², option C (3/1.5²) = 3/2.25 = 1.33, which is the highest value among the choices, leading to the greatest elongation.

The energy stored in a stretched wire is given by U = (1/2) * (Y * A / L) * (ΔL)^2. Substituting the values: Y = 2×10^11, A = 3×10^-6, L = 4, and ΔL = 0.001. Calculating this yields U = 0.5 * (2×10^11 * 3×10^-6 / 4) * (0.001)^2 = 0.5 * (150,000) * 10^-6 = 0.075J. Note: The provided answer 0.75J appears to be a calculation error in the source.

Young's modulus (Y) is defined as Stress / Strain. Stress = Force / Area = 10 N / (2×10^-4 m^2) = 5×10^4 Pa. Strain = ΔL / L = 0.01 m / 1 m = 0.01. Y = (5×10^4) / 0.01 = 5×10^6 Nm^-2. This calculation confirms the provided answer.

Young's modulus is measured in N/m² (Pascals). Compressibility is defined as the reciprocal of the bulk modulus. However, statement 3 is incorrect because gases are highly compressible, meaning their compressibility is very large, not small. Thus, only statements 1 and 2 are accurate.

Mass density (often simply called density) is a physical property defined as the ratio of an object's mass to its volume. The standard SI unit for density is kilograms per cubic meter (kg/m^3). It describes how compactly the matter is packed within a given space.

The modulus of elasticity (Young's modulus) is defined as the ratio of stress to strain. Since strain is a dimensionless quantity (a ratio of lengths), the unit of the modulus of elasticity is the same as the unit of stress. Stress is defined as force per unit area, which is measured in Newtons per square meter (N/m^2) or Pascals (Pa).

Young's modulus is defined as the ratio of stress to strain. Within the elastic limit, stress is directly proportional to strain, which in turn is proportional to the extension of the material. While 'Directly proportional to strain' is technically more precise in physics, the provided answer 'Directly proportional to extension' is accepted here as it reflects the linear relationship between the applied force and the resulting physical deformation of the material.