We report measurements of the change in electrorheological response of the low molar mass nematic pentylcyanobiphenyl (5CB) on dissolution of small amounts of a side-chain liquid crystal polymer (SCLCP). From the ratio of the intrinsic viscosities with the field on and off, [eta(on)] and [eta(off)] respectively, we deduce a value for the ratio of the rms end-to-end distances of the SCLCP parallel and perpendicular to the nematic director, R-vertical bar vertical bar/R-perpendicular to = 1.17 +/- 0.02 via application of the Brochard hydrodynamic model, which indicates that the polymer has a slightly prolate shape. Small-angle neutron scattering measurements reveal a numerically similar value for the corresponding ratio of apparent rms radii of gyration, R-g vertical bar vertical bar/R-g perpendicular to = 1.12 +/- 0.06, for the SCLCP dissolved in deuterated 5CB. Observations of the shear stress transient response of a homeotropic monodomain indicate that, at a concentration between 0.01 and 0.02 g/mL, the solution exhibits a transition from director-aligning to director-tumbling behavior. This result is inconsistent with the Brochard model, which predicts such a transition only for a polymer with an oblate shape but agrees with a modified version, which assumes an additional contribution to viscous stress arises due to elastic coupling between the solvent and polymer directors.