a
\(\begin{array}{l}
Let\,a\,be\,the\,acceleration\,of\,mass\,{m_2}\\
in\,the\,downward\,direction.\,\,Then\\
T - {m_2}\left( {g/2} \right) = {m_1}a\,\,\,\,\,\,\,\,...\left( i \right)\\
and\,{m_2}g - T = {m_2}a\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} \right)\\
Adding\,eqs.\,\left( 1 \right)\,and\,\left( 2 \right),\,we\,get\\
\left( {{m_1} + {m_2}} \right)a = {m_2}g - {m_2}\left( {g/2} \right) = {m_2}g/2\\
\therefore \,a = \frac{{{m_2}g}}{{2\left( {{m_1} + {m_2}} \right)}}
\end{array}\)