A thin-walled (thickness << radius), hollow shaft of length 1 m and mean radius, R = 5 cm has to be designed such that it can transmit a torque, T = 7 kN·m. A survey of different commercially available materials was made and following data was obtained from the suppliers (E: Young’s modulus, τ_y: yield stress in shear, ρ: density): If you assume a factor of safety of 2, what should be the approximate thickness of such a shaft?