Two-Block System (Maximum Force Without Relative Sliding)

Find the maximum external force that can be applied to a system of stacked or adjacent blocks so they move together without relative slipping.

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Two blocks $A$ and $B$ of masses $m _ { A } = 1 \mathrm {~kg}$ and $m _ { B } = 3 \mathrm {~kg}$ are kept on the table as shown in figure. The coefficients of friction between $A$ and $B$ is 0.2 and between $B$ and the surface of the table is also 0.2 . The maximum force F that can be applied on B horizontally, so that the block A does not slide over the block B is : [Take $\mathrm { g } = 10 \mathrm {~m} / \mathrm { s } ^ { 2 }$ ]
(1) 16 N
(2) 12 N
(3) 40 N
(4) 8 N