Question

Calculate Poisson ratio of aluminium , if Young's modulus of aluminium is 7*10*10 N\m2 and modulus of rigidity is 2.5*10*10 N\m2

Answer 1

Solution:

Given: Initial length of wire = L =  1 m, Diameter of wire = 2 mm, Radius of wire = 2/2 = 1 mm = 1 × 10-3 m, Load attached = m = 40 kg, Young’s modulus of material = Y = 7 × 1010N/m².

To Find: Stress = ?, Strain = ?, Force constant = ?

Stress = F / A  = mg /π r²
∴  Stress =  ( 40 × 9.8) /(3.142 ×(1 × 10-3)²)
∴  Stress =  ( 40 × 9.8) /(3.142 ×  1 × 10-6)
∴  Stress =  1.25 × 108    N/m²
Now, Y = Stress / Strain
∴   Strain = Stress / Y  =  1.25 × 108  / 7 × 1010
∴   Strain = 1.78 × 10-3
Now, Strain = l /L
∴ extension = l = Strain × L
∴  l = 1.78 × 10-3 × 1
∴  l = 1.78 × 10-3 m
Now, force constant K = F/l = mg/l = ( 40 × 9.8) /(1.78 × 10-3)
Force constant K = 2.2 × 105  N/m
Ans: Stress =  1.25 × 108    N/m²,  Strain = 1.78 × 10-3,  Force constant = 2.2 × 105  N/m


I hope it will help you dear friend...