Stress is defined as force per unit area. Doubling the diameter increases the area by a factor of four, thus reducing the stress.

Tensile stress is given by force/area. Halving the radius reduces the area by a factor of four, thus the stress quadruples for the same force.

The fractional change in volume is given by ΔV/V = ΔP/B. Here, ΔP = 50 MPa = 0.05 GPa, so ΔV/V = 0.05/200 = 0.00025.

The fractional change in volume ΔV/V is given by ΔV/V = ΔP/B, where ΔP = 10 MPa and B = 200 GPa, resulting in 0.00005.

The change in volume ΔV/V = P/B, so ΔV/V = 50 MPa / 200 GPa = 0.025%.

Poisson's ratio is defined as the negative ratio of lateral strain to longitudinal strain, so a Poisson's ratio of 0.3 means the ratio is 0.3.

A material is considered elastic if it returns to its original shape after the removal of the applied stress.

Young's modulus (Y) = Stress / Strain = 100 MPa / 0.002 = 50 GPa.

A Poisson's ratio of 0.5 indicates that the material is incompressible.

According to Hooke's law, elongation is inversely proportional to the spring constant; thus, if the spring constant is doubled, the elongation halves.

Using Hooke's law, k = F/x = 10 N / 0.05 m = 200 N/m.

The extension of the wire can be calculated using the formula: extension = (F * L) / (A * Y).

The elongation ΔL of a wire is given by ΔL = FL / (AE), where E is Young's modulus.

The elongation ΔL of a wire is given by ΔL = (F * L) / (A * Y), where Y is Young's modulus.

A linear stress-strain relationship indicates that the material behaves elastically within the limit of proportionality.

Plastic deformation means that the material does not return to its original shape after the load is removed.

A high shear modulus indicates that the material is very stiff and resists shear deformation.

A Poisson's ratio of 0.3 indicates that the material will contract laterally when stretched.

A Poisson's ratio of 0.3 means that the lateral strain is 0.3 times the axial strain.

A Poisson's ratio of 0.3 implies that the material contracts laterally when stretched.

A high Young's modulus indicates that the material is very elastic.

When a material is stretched beyond its elastic limit, it undergoes permanent deformation and does not return to its original shape.

Strain is defined as the change in length divided by the original length, so 2% = 0.02.

The elongation (ΔL) can be expressed as ΔL = F * L / (A * E).

Young's modulus is a material property and does not change with the dimensions of the wire.

Stress = Young's modulus × Strain = 150 GPa × 0.01 = 150 MPa.

According to Hooke's Law, if stress is doubled, strain also doubles for elastic materials.

Generally, the Young's modulus of materials decreases with an increase in temperature.

Strain = Stress / Young's modulus = 200 MPa / 100 GPa = 0.002.

The total strain energy stored in a volume V is given by the product of strain energy density U and volume V, i.e., Total Energy = U * V.