$(5+10$ marks$)$ A lawn sprinkler with two nozzles $5$ mm in diameter, each at a distance of $0\mathrm{.}15$ m and

$0\mathrm{.}2$ m from a central tap $($see Fig. $2),$ is capable of discharging $6$ litres$/$minute$.$ The nozzles discharge

water upwards and outwards from the plane of rotation. What torque will the sprinkler exert on the

hand, if the sprinkler is held stationary, and at what angular velocity $$ will it rotate freely?

Fig. $2$