Water having a density of $$1000\,\,kg/{m^3},$$ issues from a Nozzle with a velocity of $$10$$ $$m/s$$ and the jet strikes a bucket mounted on a Pelton wheel. The wheel rotates at $$10$$ $$rad/s$$. The mean diameter of the wheel is $$1$$ $$m.$$ The jet is split into two equal streams by the bucket; such each stream is deflected by $${120^ \circ }$$, as shown in the figure. Friction in the bucket may be neglected. Magnitude of the torque exerted by the water on the wheel, per unit mass flow rate of the incoming jet, is