A machine member is subjected to fluctuating stress, $$σ = σ_0$$ cos(5π t). The endurance limit of the material is 350 MPa and the yield strength is 500 MPa. If the factor of safety used in the design is 3.5, then the maximum allowable stress $$σ_0$$​ in MPa according to soderberg fatigue criteria is

Correct option is C

​$$\begin{aligned}&\textbf{Given:} \\&\text{Fluctuating stress: } \sigma = \sigma_0 \cos(5\pi t) \\&\quad \bullet \text{Stress amplitude: } \sigma_a = \sigma_0 \\&\quad \bullet \text{Mean stress: } \sigma_m = 0 \quad (\text{purely alternating stress}) \\&\text{Endurance limit } (\sigma_e): 350 \, \text{MPa} \\&\text{Yield strength } (\sigma_y): 500 \, \text{MPa} \\&\text{Factor of safety (FOS): } 3.5 \\[1em]&\textbf{Soderberg Fatigue Equation} \\&\text{The Soderberg criterion for combined alternating and mean stresses is:} \\&\frac{\sigma_a}{\sigma_e} + \frac{\sigma_m}{\sigma_y} = \frac{1}{\text{FOS}} \\&\text{For purely alternating stress } (\sigma_m = 0): \\&\frac{\sigma_0}{\sigma_e} = \frac{1}{\text{FOS}} \\[1em]&\textbf{Solve for } \sigma_0 \\&\text{Substitute the given values:} \\&\frac{\sigma_0}{350} = \frac{1}{3.5} \\&\Rightarrow \sigma_0 = \frac{350}{3.5} = \boxed{100 \, \text{MPa}}\end{aligned}$$​​