A thinwalled tube is subject to a torque T. The only nonzero stress component is the shear stress \(\tau_{x y}\), which is given by \(\tau_{x y}=10,000 T(\mathrm{~Pa})\), where \(T\) is the torque in N.m. When the yield strength \(\sigma_{Y}=300 \mathrm{MPa}\) and the safety factor \(N=2\), calculate the maximum torque that can be applied using:

a. maximum principal stress criterion (Rankine);

b. maximum shear stress criterion (Tresca); and

c. distortion energy criterion (Von Mises).