The maximum value of mass of block C (in kg) 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 μ=0.3; g=10m/s2.)

Maximum friction that can be obtained from A to B isf1≡μm1g=(0.3)(100)(10)=300NAnd maximum friction between B and ground isf2=μmA+mBg=(0.3)(100+140)(10)=720NDrawing free body diagram of A, B and C in limiting caseEquilibrium of A gives T1=f1=300N                 …(i)Equilibrium of B gives 2T1+f1+f2=T2or T2=2(300)+300+720=1620N                 …(ii)and equilibrium of C gives mαg=T2 or 10mc=1620or mc=162kg