Two boxes are attached by a taut line that is threaded over a pulley of radius $16$ cm and mass $106$ g$.$ The larger box has a mass of $773$ g and lays on a level surface with friction coefficient $0\mathrm{.}19.$ The smaller box has a mass of $365$ g and sits on a frictionless incline of grade $1\mathrm{.}06.$

$($a$)$ What is the acceleration of the boxes?

$($b$)$ What is the maximum mass for the larger block so that it slides?

$($c$)$ If the pulley were massless, what would the acceleration of the boxes be$?$

$($b$)$ What is the maximum mass for the larger block so that it slides with the massless pulley?