What is the largest mass of  $C$ in $\mathrm{kg}$ that can be suspended without moving blocks  $A$ and $B$?. The static coefficient of friction for all plane surface of contact is $0.3$. Mass of block $A$ is $(50 \mathrm{kg})$and block Bis ($70 Kg$). Neglect friction in the pulleys. 

Maximum value of friction between $A$ and $B$

${\left(f_1\right)}_{\max }=\mu {\mathrm{N}}_1=)\mu {\mathrm{m}}_{1g}$

$$\begin{gathered} =0.3\times 50\times 10 \\ =150 \mathrm{N} \end{gathered}$$

Maximum value of friction between $B$ and ground

$$\begin{gathered} {\left(f_2\right)}_{\max }=\mu N_2=\mu \left(m_1+m_3\right)g \\ =(0.3)\left(120\right)\left(10\right)=360 \mathrm{N} \end{gathered}$$

Force diagram is as shown below

$$\begin{gathered} T_1 \\ \therefore m_{2}g \\ {T}_2={\left(f_1\right)}_{\max }=150 \mathrm{N} \\ {T}_1=2T_2+{\left(f_1\right)}_{\max }+{\left(f_2\right)}_{\max } \\ =300+150+360=810 \mathrm{N} \\ {T}_1=m_{2}g \\ {m}_c=\frac{T_1}{g}=\frac{810}{10}=81 kg \end{gathered}$$