The radius of the bar's circular cross section varies linearly from 10 mm at x=0 to 5 mm at x = 150 mm. The shear modulus of the material is G= 17 GPa. Suppose that the torque T at the end of the bar is 20 N-m and you want to apply a torque in the opposite direction at x = 75 mm so that the angle through which the end of the bar rotates is zero. What is the magnitude of the torque you must apply?

30 mm? y 150 mm T Problems 4.60-4.62 section varies linearly