A cylindrical rod of radius 7mm and Young’s Modulus 70 GPa has a weight F applied to it. The material experiences a strain of 0.2%. What force has been applied?

Young's Modulus is defined as the ratio of stress to strain. E = stress/strain. Stress is the force per unit area, F/A. By substitution, we can see that E = F/(A x strain). Rearranging gives F = E x A x strain. Now it is case of evaluating the expression F = 70x10⁹ x ( π x (7x10^-3)²) * 0.2x10^-2 = 21551 N. It is important to remember that the strain is given as a percentage, but needs to be evaluated as a ratio of extension to length; i.e. as a decimal.