A system consists of three masses m_1, m_2 and m_3 connected by a string passing over a pulley P. The mass m_1 hangs freely and m_2 and m_3 are on a…

A system consists of three masses $\displaystyle \mathrm{m}_1, \mathrm{~m}_2$ and $\displaystyle \mathrm{m}_3$ connected by a string passing over a pulley P. The mass $\displaystyle \mathrm{m}_1$ hangs freely and $\displaystyle \mathrm{m}_2$ and $\displaystyle \mathrm{m}_3$ are on a rough horizontal table (the coefficient of friction $\displaystyle =\mu$). The pulley is frictionless and of negligible mass. The downward acceleration of mass $\displaystyle \mathrm{m}_1$ is : (Assume $\displaystyle \mathrm{m}_1=\mathrm{m}_2=\mathrm{m}_3=\mathrm{m}$)