flem $2$: The gear train shown below has $4$ gears where gear $1$ and $4$ are mounted on the same shaft the pinion $1$ is rotating clockwise driving gear $2$ which is meshed with gear $3$ to provide torque to the eutput shaft a$.$ Gears $1,2,$ and $3$ have module of $10$ mm and $\backslash (20^\{\backslash$circ$\}\backslash )$ pressure angle. The pinion $1$ rotates at $800$ rpm and transmits $4$ kW of power.

$($a$)$ Draw the complete free body diagram of gear $2$ showing all the contact forces and shaft forces. $\backslash ((4\backslash )$ points$)$

$($b$)$ Assuming $100\backslash \%$ efficient power transmission, calculate the forces exerted by shaft b on gear $2$ along x and y directions. $(12$ points$)$

$($c$)$ If the pitch circle radius of gear $4$ is $375$ mm $,$ then, if required for a different purpose, can gear $1$ and $4$ be meshed with both having the same pressure angle? Explain. $(2$ points$)$

$(18$ points$)$