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 f1=μmAg= 0.3 100 10= 300 N and maximum friction between B and ground is f2=μmA+ mBg= 0.3100 + 140 10 = 720 NDrawing free-body diagrams of A, B and C in limiting caseEquilibrium of A gives T1= f1= 300NEquilibrium of B gives 2T1+ f1+ f2= T2 or T2=2300 + 300 + 720 = 1620 Nand equilibrium of C gives mCg=T2or 10mC= 1620 or mC = 162 kg