In figure, the coefficient of friction between the floor and the block $B$ is $0.2$ and between blocks $A$ and $B$ is $0.3$. ........ $N$ is the maximum horizontal force $F$ can be applied to the block $B$ so that both blocks move together .
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Common acceleration is
$a=\frac{\mu_{A} m_{A} g}{m_{B}}=0.3 \times 10$
$a=3 \mathrm{m} / \mathrm{s}^{2}$
and
$\mathrm{F}-0.2(20+40) \mathrm{g}=(20+40) \mathrm{a}$
$\Rightarrow \mathrm{F}-120=60 \times 3$
$\Rightarrow \mathrm{F}=300 \mathrm{N}$
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