The maximum value of $F$ which can be applied on the system shown in figure so that both blocks move together with same acceleration is ..........
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(d)
Let both blocks move together with acceleration a. making $FBD$ of $m-2$ block for vertical balance
$M=M_2\,g$
$\Rightarrow fr =\mu M _2\,g$
$\Rightarrow a =\frac{ fr }{ M _2}=\mu g \ldots \ldots .(1)$
making FBD of second block
$F-f r=M_1 a$
$F-\mu m_2 g=M_1(\mu g )$
$\Rightarrow F=\mu\left[M_1+M_2\right]\,g$
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