A circular object of radius r rolls without slipping on a horizontal level floor with the center having velocity $$V$. The velocity at the point of contact between the object and the floor is

Water flows through a pipe having an inner radius of $$10$$ $$mm$$ at the rate of $$36$$ $$kg/hr$$ at $${25^ \circ }C$$. The viscosity of water at $${25^ \circ }C$$ is $$0.001$$ $$kg/m.s.$$ The Reynolds number of the flow is ____________________

For a fully developed flow of water in a pipe having diameter $$10$$ $$cm,$$ velocity $$0.1$$ $$m/s$$ and kinematic viscosity $${10^{ - 5}}\,\,{m^2}/s,$$ the value of Darcy friction factor is ________________

In a simple concentric shaft-bearing arrangement, the lubricant flows in the $$2$$ $$mm$$ gap between the shaft and the bearing. The flow may be assumed to be a plane Couette flow with zero pressure gradient. The diameter of the shaft is $$100$$ $$mm$$ and its tangential speed is $$10$$ $$m/s.$$ The dynamic viscosity of the lubricant is $$0.1$$ $$kg/m.s.$$ The frictional resisting force (in newton) per $$100$$ $$mm$$ length of the bearing is ______________.