hi ,

in this question poin to consider is that , block 2m is not involed in any type of motion, it wil remain unmoved . so for no slipping  block m should also be at rest

 consider block m,

  net force on it should be zero,

 T - μmg = 0

T = F ,so

μ =  F /mg , it will be its min. value (a)

Hi,

Sorry for that,

actually I didn't consider the other block 

if see in the fig ,

the max accelaration of the combined system of both block =  F/3m

now we hav to find the u for this condition

total horz. force on the block 2 =>   umg - F =m*F/3m =F/3

                                          =>umg = 4F/3

                                         =>u(min.)=4F/3mg

minimum u value ensure no slipping at all,  maens that the both block will move together for that given  value of FORCE

I really appreciate ur move bcz of  which i cud correct my mistake

ENJOY the  solution