question_answer

The maximum value of mass of block C so that neither A nor B moves is (Given that mass of .4 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 \[\mu =0.3;\] \[g=10\,m/{{s}^{2}}\])

A) \[210\,kg\]               

B) \[190\,kg\]               

C) \[185\,kg\]               

D) \[162\,kg\]

Correct Answer: D

Solution :

[d] Maximum friction that can be obtained between A and B is \[{{f}_{1}}=\mu {{m}_{A}}g=(0.3)(100)(10)=300N\] and maximum friction between B and ground is \[{{f}_{2}}=\mu ({{m}_{A}}+{{m}_{B}})g=(0.3)(100+140)(10)=720N\]Drawing free body diagrams of A, B and C in limiting case, we get Equilibrium of A gives \[{{T}_{1}}={{f}_{1}}=300N\]                          ...(1) Equilibrium of B gives \[2{{T}_{1}}+{{f}_{1}}+{{f}_{2}}={{T}_{2}}\] or \[{{T}_{2}}=2(300)+300+720=1620N\]         ?..(2) and equilibrium of C gives \[{{m}_{C}}g={{T}_{2}}\] or         \[10{{m}_{C}}=1620\] or         \[{{m}_{C}}=162kg\]