A round bar 40 mm dia meter is subjected to an axial pull of 80 kn and reduction in diameter was found to be 0.00775mm.find poisson's ratio and young's modules for the material of the bar. take value of shear modules as 40kn/mm square. [Please Solve it describtively in long form & not in short form]

99.2mpa

To find Poisson's ratio and Young's modulus for the material of the bar, we need to use the given information:

- Diameter of the bar (D) = 40 mm
- Axial load (P) = 80 kN
- Reduction in diameter (∆D) = 0.00775 mm
- Shear modulus (G) = 40 kN/mm^2

Firstly, let's calculate the original cross-sectional area of the bar:
A = (π/4) * D^2
A = (π/4) * (40 mm)^2
A = 1256.64 mm^2

Next, we need to determine the change in cross-sectional area (∆A) due to the axial pull. The change in diameter (∆D) can be used to calculate ∆A:
∆A = (π/4) * (∆D)^2
∆A = (π/4) * (0.00775 mm)^2
∆A = 0.00004741 mm^2

Now, we can find the value of the Poisson's ratio (ν). The formula to calculate Poisson's ratio is:
ν = (∆D/D) / (∆L/L)
where ∆L is the change in length and L is the original length.

Here, we are not given the change in length (∆L), but we are given the axial load (P). We can assume that the cross-sectional area of the bar remains constant, so we can use the formula:
∆L = (P * L) / (A * E)
where E is the Young's modulus.

Now, let's rearrange the formula for ∆L to solve for Young's modulus:
E = (P * L) / (A * ∆L)

Firstly, we need to convert the axial load (P) from kN to N:
P = 80 kN = 80,000 N

Next, we need to determine the original length (L) of the bar. Unfortunately, the given information does not provide the information about the original length. You would need to know the original length or be given additional information to proceed further in calculating the Young's modulus.

In summary, to find the Poisson's ratio and Young's modulus for the material of the bar, we need the original length of the bar. Without that information, it is not possible to calculate these values.