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 the of B `140 kg`. Pulleys are smooth and friction coefficient between A and B and horizontal surface `mu = 0.3)`(Taking` g = 10 ms^(-2))`

Options

A. `210 kg`
B. `190 kg`
C. `185 kg`
D. `162 kg`

Answer

d

Explanation

Maximum friction that can be abtained between A and B is `f_(1) = mu m_(A)g = (0.3)(100) = 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 of A,B and C in limiting case

Equilibrium of A given
`T_(1) = f_(1) = 300N`...(i)
Equilibrium of B given
`2T_(1) = f_(1) + f_(2) = T_(2)`
or `T_(2)= 2(300) + 300 + 720 = 1620 N`...(ii)
and equilibrium of C gives `m_(c)g = T_(2)`
or `10 m_(c) = 1620` or `m_(c) = 162 kg`