  We discuss the observable-dependence of the effective temperature $T_{eff}$,
defined via the fluctuation-dissipation relation, of an out-of-equilibrium
system composed by homonuclear dumbbell molecules. $T_{eff}$ is calculated by
evaluating the fluctuation and the response for two observables associated
respectively to translational and to rotational degrees of freedom, following a
sudden temperature quench. We repeat our calculation for different dumbbell
elongations $\zeta$. At high elongations ($\zeta > 0.4 $), we find the same
$T_{eff}$ for the two observables. At low elongations ($\zeta \leq 0.4$), only
for very deep quenches $T_{eff}$ coincides. The observable-dependence of
$T_{eff}$ for low elongations and shallow quenches stresses the importance of a
strong coupling between orientational and translational variables for a
consistent definition of the effective temperature in glassy systems.
