hi, 
if both boxes move together their acceleration,
   a = F / (m+M)
 for big box , it will move only due to friction force
 it moves with max accel. when the friction will be max.
    a M =  µ. mg  / M                                                        ( max friction =   µ. mg  )
 if both boxes move together ,
 a =  a M 
 F / (m+M) = µ. mg  / M     
 F =  (m+M) µ. mg  / M     
 it will be the max force for both the boxes move together
 
						

							
forces on block M and m are

on balancing forces we get,
N2 =mg
N = N2 +Mg
F-f=ma
f=Ma
so from above
F = (m+M)a
putting above gives : umg = Ma
so   F=u(M+M)mg / M
where u is coeff. of friction btn teo blocks
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