Physics - Error Question with Solution | TestHub

Let $f_1$ and $f_2$ be the friction force between A and B and between B and horizontal surface respectively. Limiting values if these frictional forces will be

$$\begin{array}{rlr}& f_{L_1}=0.3\times 50\times 10=150\mathrm{N}& f_{L_2}=0.3\times 120\times 10=360\mathrm{N}\end{array}$$

The FBD of the three blocks are shown in figure Let m is the mass of block C . For A and B to remain at rest, block C should also remain at rest For blockC : $\mathrm{T}=\mathrm{mg}$ For block A: $T_1=f_1$ For block B: $T=f_1+f_2+2T_1$ For largest value of mass of C , the friction $f_2$ must be towards left

$$\begin{array}{rlr}& T=3f_1+f_2=mg& f_1\le f_{L_1}\&f_2\le f_{L_2}\end{array}$$

Hence $mg\le f_{L_1}+f_{L_2}$ or $m\le 81$ ∴ maximum value of $\mathrm{m}=81\mathrm{kg}$