Find out the range of force in which both the blocks move together.

Explanation

If `f_(1)` is friction force between block A & lower surface and `f_(2)` is fricton force between both the block's surface.
F.B.D.

`f_("1 max") =mu_(1) N_(1) = ( 0.1) ( 60) = 6 N `
`f_("2 max") = mu_(2) N_(2) = ( 0.5 ) ( 20) = 10 N`
Upper 2 kg block is move only due to friction force so maximum acceleration of that block is
`a_("max") =(10)/( 2) = 5 m//s^(2)`
This is the maximum acceleration for which both the blocks will move together.
Therefore for `a le 5 ms^(-2)` we can take both the bloks as one system.
F.B.D.
For `F lt 6N`. Blocks will not move at all. Now the value of `F_("max")` for which both the blocks will move together.
`F_("max") -6 = 6 xx5 `
`F_("max") = 36N `
Conclusion if
`0 N lt F lt 6N` No blocks will move
`6N lt F lt 36 N` Both blocks will move together
`F gt 36N ` Both move separately.