The shearing moment acting on the cylinder, causes shear stress (check the definition of shear modulus here) resulting in the cylinder to twist and thus in a shear strain. As the cylinder twists
an angle
resulting in the upper surface to shift a distance of 
relative to the lower surface as shown in the figure. Thus, the shear strain is given by 
. This, shear strain will result in a shear stress acting tangential to the surface given by
. The net tangential force acting on the cylinder is given by the stress times the area of cross section given by,
Since this force acts at a distance r from the axis, the twisting moment is given by,
b)
For this part consider an infinitesimally thin vertical section of the solid cylinder at a distance x from the center and of thickness dx. As solved in part a of the problem, the twisting moment acting on this section will be given by,
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