  Using a data set corresponding to an integrated luminosity of $3 fb^{-1}$,
collected by the LHCb experiment in $pp$ collisions at centre-of-mass energies
of 7 and 8 TeV, the effective lifetime in the $B^0_s \rightarrow J/\psi \eta$
decay mode, $\tau_{\textrm{eff}}$, is measured to be $\tau_{\textrm{eff}} =
1.479 \pm 0.034~\textrm{(stat)} \pm 0.011 ~\textrm{(syst)}$ ps. Assuming $CP$
conservation, $\tau_{\textrm{eff}}$ corresponds to the lifetime of the light
$B_s^0$ mass eigenstate. This is the first measurement of the effective
lifetime in this decay mode.
