Asolid and a hollow shaft of the same material must transmit the same maximum torque? ?

Answer with explanation:

Using the relationship between the Torque and shear stress developed we have

Now since the material is same thus we conclude that 'G' of both the materials is same

Thus torque maximum torque is transmitted at the point when the material of the shaft just begin's to fail

In the case of faliure we have

Using this principle we conclude from the equation of torsion

Now it is reasonable to compare shafts of same parameter's thus assuming both the shafts have the same area thus for hollow shaft it has to be distributed away from the center as it is hollow. Thus as compared to the solid shaft with same cross sectional area  Polar moment of inertia   of hollow shaft will be more thus according to the above equation it will transmit more torque as compared to a solid shaft of same cross sectional area and material.

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