A vertical metal cylinder of radius 2 cm and length 2 m is fixed at its lower end, and a load of 100 kg is placed on it. Determine the strain. The Young modulus of the metal is 2 10¹¹ N/m ^2 .

Step-by-step solution

Given: Radius of the cylinder, r = 2 cm = 2 10⁻² m Mass of the load, m = 100 kg Young's modulus, Y = 2 10¹¹ N/m ^2 Acceleration due to gravity, g 10 m/s ^2 The force applied on the cylinder is: F = mg = 100 10 = 1000 N The cross-sectional area of the cylinder is: A = r^2 = (2 10⁻²)^2 = 4 10⁻⁴ m ^2 The strain is given by the formula: Strain = Stress Y = F AY Substituting the values: Strain = 1000 4 10⁻⁴ 2 10¹¹ Strain = 1000 8 10^7 = 1 8 10⁻⁴ Using 3.14 : Strain 1 25.12 10⁻⁴ 0.0398 10⁻⁴ 4 10⁻⁶