A hollow shaft (d₀ = $$2$$d_i, where d₀ and d_i are the outer and inner diameters respectively) needs to transmit $$20$$ kW power at $$3000$$ RMP. If the maximum permissible shear stress is $$30$$MPa, d₀ is

Consider a simply supported beam of length $$50$$h, with a rectangular cross-section of depth h, and width $$2$$h. The beam carries a vertical point load P, at its mid-point. The ratio of the maximum shear stress to the maximum bending stress in the beam is