A hollow aluminum tube used in a roof structure has an outside diameter d2 = 104 mm and an inside diameter d1 = 82 mm (see figure). The tube is 2.75 m long, and the aluminum has shear modulus G = 28 GPa.
(a) If the tube is twisted in pure torsion by torques acting at the ends, what is the angle of twist (in degrees) when the maximum shear stress is 48 MPa?
(b) What diameter d is required for a solid shaft (see figure) to resist the same torque with the same maximum stress?
(c) What is the ratio of the weight of the hollow tube to the weight of the solid shaft?

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