A laparoscopic tool consists basically of a long, thin shaft with a gripper at the end. Its shaft is a hollow tube through which a wire is used to actuate the gripper. Derive a performance index for a light, stiff, thin-walled tube of this type under bending loads. Consider the diameter to be fixed and the tube thickness to be the free variable. [Hint: use the fact that this is a thin-walled tube to obtain a simplified moment of inertia expression for use in deriving the performance index.]