In the given problem let us first take m₂  as the system ( Step no1)

The forces acting on this system are: (step 2)



                1. Weight m₂g in the vertically downward direction.

                2.Tension T of the string in the vertically upward direction.



So the net downward force is   m₂g--T. This force accelerates the body in the downward direction with accln a ( say ).

As I cant draw i skip step3.

now step 4.

the equn is Force = mass* accln                   

                     m₂g -- T = m₂a  ..........................(1)

Apply the same process by taking m₁  as a system.

List all forces.These are:

                                    1. wt. m₁g vertically downward.

                                    2. Tensin T up the inclined plane along the string.                                              3. Frictional force down the inclined plane (f)

Net upward force along the plane T - m₁g sin alpha - f .

    Here we have resolved m₁g perpendicularly to inclined plane as  m₁g cos alpha ( downward) and along the plane m₁g sin alpha ( opposite to direction of tension T i,e, down the inclined plane).           

                                    Draw FBD.



Now this body moves up the inclined plane. Equn is

                        T - m₁g sin alpha - f = m₁ a      ............................(2)

now solve.

g = 10 m/s²

alpha = 30 degree         

 f on m₁ = 0.1 * m₁ * g cos (alpha)     [ remember friction= mu* normal reaction]    



From these two equns find result.