  The particle momentum anisotropy ($v_n$) produced in relativistic nuclear
collisions is considered to be a response of the initial geometry or the
spatial anisotropy $\epsilon_n$ of the system formed in these collisions. The
linear correlation between $\epsilon_n$ and $v_n$ quantifies the efficiency at
which the initial spatial eccentricity is converted to final momentum
anisotropy in heavy ion collisions. We study the transverse momentum, collision
centrality, and beam energy dependence of this correlation for different
charged particles using a hydrodynamical model framework. The ($\epsilon_n
-v_n$) correlation is found to be stronger for central collisions and also for
n=2 compared to that for n=3 as expected. However, the transverse momentum
($p_T$) dependent correlation coefficient shows interesting features which
strongly depends on the mass as well as $p_T$ of the emitted particle. The
correlation strength is found to be larger for lighter particles in the lower
$p_T$ region. We see that the relative fluctuation in anisotropic flow depends
strongly in the value of $\eta/s$ specially in the region $p_T <1$ GeV unlike
the correlation coefficient which does not show significant dependence on
$\eta/s$.
