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 compression of the cylinder. The Young modulus of the metal is 2 10¹¹ N/m ^2 .

Step-by-step solution

The compression of the cylinder is given by the formula for Young's modulus: Y = F L A L L = F L A Y The force applied is the weight of the load. Taking g = 10 m/s ^2 : 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 Substituting the given values into the formula: L = 1000 2 4 10⁻⁴ 2 10¹¹ L = 2000 8 10^7 L = 250 10⁻⁷ m Using 3.14 : L 79.6 10⁻⁷ m 8 10⁻⁶ m