Consider the torsion of a thin-walled tube. Determine an approximate expression for the torque if the shear stress must be less than a given working stress τw. Express this result in terms of the tube's mean radius R and its thickness t. (Hint: The binomial theorem will be useful here.) Also, derive an approximate expression for the strength-toweight ratio of the tube in terms of the working stress, its radius, and length L, and its specific weight ρg. This result is widely used in aircraft design.