c
\(\begin{array}{l}
{m_2}g - T = {m_2}a\\
T - \mu k\,{m_1}g = {m_1}a\\
 \Rightarrow \,a = \frac{{\left( {{m_2} - \mu km} \right)g}}{{{m_1} + {m_2}}}\\
For\,the\,block\,of\,mass\,'m{'_2}\\
{m_2}g - T = {m_2}\left[ {\frac{{m - 2 - {\mu _k}}}{{{m_1} + {m_2}}}} \right]
\end{array}\)

\(\begin{array}{l}
g{m_2}g - T = {m_2}\left[ {\frac{{{m_2} - {\mu _k}m - 1}}{{{m_1} + {m_2}}}} \right]\\
{m_2}g = {m_2}g\left[ {\frac{{{m_2} - {\mu _k}m - 1}}{{{m_1} + {M_2}}}} \right]
\end{array}\)