Force of friction on mass m₂ = $\mu$m₂g

Force of friction on mass m₃ = $\mu$m₃g

Let a be common acceleration of the system.

$\therefore$ $a = {{{m_1}g - \mu {m_2}g - \mu {m_3}g} \over {{m_1} + {m_2} + {m_3}}}$

Here, m₁ = m₂ = m₃ = m

$\therefore$ $a = {{mg - \mu mg - \mu mg} \over {m + m + m}} = {{mg - 2\mu mg} \over {3m}} = {{g\left( {1 - 2\mu } \right)} \over 3}$

Hence, the downward acceleration of mass m₁ is ${{g\left( {1 - 2\mu } \right)} \over 3}$