$\begin{array}{l}
Here,\,{m_1} = {m_2} = {m_3} = m\\
\therefore a = \frac{{mg - \mu mg - \mu mg}}{{m + m + m}} = \frac{{mg - 2\mu mg}}{{3m}}\\
\,\,\,\,\,\,\,\, = \frac{{g\left( {1 - 2\mu } \right)}}{3}\\
Hence,\,the\,downward\,acceleration\,of\,mass\,\\
{m_1}\,is\,\frac{{g\left( {1 - 2\mu } \right)}}{3}.
\end{array}$