A 0.2 mm thick strip is bent and laid over a frictionless pulley of 25 mm diameter. If E = 100 GPa, the maximum stress in the strip is

Correct option is D

​$$\textbf{Given:} \\\text{Thickness, } t = 0.2 \ \text{mm} = 0.2 \times 10^{-3} \ \text{m} \\\text{Pulley diameter = 25 mm } \Rightarrow \text{radius } R = \frac{25}{2} = 12.5 \ \text{mm} = 12.5 \times 10^{-3} \ \text{m} \\\text{Young's modulus, } E = 100 \ \text{GPa} = 100 \times 10^9 \ \text{Pa} \\\\\textbf{Formula:} \\\sigma = \frac{Et}{2R} \\\\\text{Where:} \\\sigma = \text{maximum bending stress} \\E = \text{Young's modulus} \\t = \text{thickness of the strip} \\R = \text{radius of curvature of bending} \\\textbf{Substitute values:} \\\sigma = \frac{100 \times 10^9 \times 0.2 \times 10^{-3}}{2 \times 12.5 \times 10^{-3}} = \frac{20 \times 10^6}{25 \times 10^{-3}} \\\sigma = 0.8 \times 10^9 = \boxed{800 \ \text{MPa}}$$​​