Final answer:
The ratio of longitudinal stress to longitudinal strain in the rubber string can be obtained by calculating the stress (which is the centripetal force divided by the cross-sectional area) and dividing it by the strain (change in length over original length), which collectively represent Young's modulus (E).
Step-by-step explanation:
The student has asked for the ratio of longitudinal stress and longitudinal strain in a rubber string being whirled around horizontally while subject to a particular mass and speed. To solve for the ratio of stress to strain, which is equivalent to Young's modulus (E), we need to assess the forces involved and the resulting elongation of the rubber string.
The formula for Young's modulus is E = stress/strain, with stress = force/area and strain = ΔL/L. The force applied to the rubber string in this case would be the centripetal force needed to keep the mass moving in a circle, which can be calculated using F = m × w^2 × r, where m is the mass, w is the angular velocity, and r is the radius. Strain will be the change in length over the original length ( ΔL/L ), which can be deduced after we understand the elasticity of the rubber when the force is applied.