It would be helpful if someone could help with this problem.

Let us consider a mass m1 on a horizontal surface which has friction between the mass and the surface. It is attached to another mass m2 with the help of a string with mass m3 and length l. The mass 2 is hanged by passing over a frictionless pulley of small radius. Let m1>m2>m3. Derive an equation for the minimum distance needed by the string in the vertical position for the masses to start accelerating.

Since this question deals with a rope of a certain mass. I couldn't solve it. Links for reference to such problems are welcomed.

Thank you for your answers.