The maximum value of mass of block C so that neither A nor B moves is (given that mass of A is 100 kg and that of B is 140 kg. Pulleys are smooth and friction coefficient between A and B and between B and horizontal surface is m= 0.3) (Take g = 10ms^-2 ).

 

Maximum friction that can be obtained between A and B is $f_1=\mu m_{A}g=\left(0.3\right)\left(100\right)\left(10\right)$= 300 N and maximum friction between B and ground is $f_2=\mu \left(m_A+m_B\right)g=\left(0.3\right)\left(100+140\right)\left(10\right)=720N$

Drawing free-body diagrams of A, B and C in limiting case

Equilibrium of A gives $T_1=f_1=300N$

Equilibrium of B gives $2T_1+f_1+f_2=T_2$ $or T_2=2\left(300\right)+300+720=1620N$

and equilibrium of C gives $m_{C}g=T_2$

$or 10m_C= 1620 or m_C = 162 kg$