  We report the experimental details of how mechanical detwinning can be
implemented in tandem with high sensitivity nuclear magnetic resonance
measurements and use this setup to measure the in-plane anisotropy of the
spin-lattice relaxation rate in underdoped Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$
with $x=0.048$. The anisotropy reaches a maximum of 30\% at $T_{N}$, and the
recovery data reveal that the glassy behavior of the spin fluctuations present
in the twinned state persist in the fully detwinned crystal. A theoretical
model is presented to describe the spin-lattice relaxation rate in terms of
anisotropic nematic spin fluctuations.
