An aluminum tube has an inside diameter d₁ = 50 mm, shear modulus of elasticity G = 27 GPa, n = 0.33, and torque T = 4.0 kN ? m. The allowable shear stress in the aluminum is 50 MPa, and the allowable normal strain is 900 X 10^-6.

(a) Determine the required outside diameter d₂.

(b) Re-compute the required outside diameter d₂ if the allowable normal stress is 62 MPa and the allowable shear strain is 1.7 X 10^-3.