  Within the effective Lagrangian approach, we carry out a unified study of the
$J/\psi (\psi')\to VP$, $J/\psi \to P\gamma$ and relevant radiative decays of
light-flavor hadrons. Large amount of experimental data, including the various
decay widths and electromagnetic form factors, are fitted to constrain the
numerous hadron couplings. Relative strengths between the strong and
electromagnetic interactions are revealed in the $J/\psi \to VP$ and $\psi' \to
VP$ processes. The effect from the strong interaction is found to dominate in
the $J/\psi \to \rho\pi$ decay, while the electromagnetic interaction turns out
to be the dominant effect in $\psi' \to \rho\pi$ decay, which provides an
explanation to the $\rho\pi$ puzzle. For the $J/\psi\to
K^{*}\bar{K}+\bar{K}^{*}K$ and $\psi' \to K^{*}\bar{K}+\bar{K}^{*}K$, the
former process is dominated by the strong interactions, and the effects from
the electromagnetic parts are found to be comparable with those of strong
interactions in the latter process. Different $SU(3)$ breaking effects from the
electromagnetic parts appear in the charged and neutral channels for the $\psi'
\to K^{*}\bar{K}+\bar{K}^{*}K$ processes explain the rather different ratios
between $B(\psi'\to K^{*+}K^{-}+K^{*-}K^{+})/B(J/\psi\to
K^{*+}K^{-}+K^{*-}K^{+})$ and $B(\psi'\to
K^{*0}\bar{K}^{0}+\bar{K}^{*0}K^{0})/B(J/\psi\to
K^{*0}\bar{K}^{0}+\bar{K}^{*0}K^{0})$.
