The inputs to a certain hydrostatic drive include torque of $250$ Nm and speed of $2500$ rpm $.$ The drive includes a variable displacement pump, the displacement of which can vary from $42c\frac{m^3}{r}ev$ to $0$ to $42c\frac{m^3}{r}ev$ in the opposite direction. Assume the volumetric efficiency of the pump and motor are each $0\mathrm{.}97,$ while the torque efficiencies are each $0\mathrm{.}93.$ The maximum permissible pressure drop across the motor is $35$ MPa $.$ If the motor has fixed displacement of $42c\frac{m^3}{r}ev,$ calculate the maximum $($a$)$ motor speed, $($b$)$ motor torque, $($c$)$ output power, and $($d$)$ transmission efficiency $--$ that is$,$ output power divided by input power. Recalculate the $($e$)$ motor speed, $($ f $)$ motor torque, and $($ g $)$ output power when the pump displacement is reduced to $4\mathrm{.}2c\frac{m^3}{r}ev.(35)$