A horizontal water jet strikes a block of mass 5 kg resting on a rough horizontal surface. The water falls vertically downwards immediately after striking the block. The coefficient of static friction between the block and the surface is 0.4 . If the velocity of the water jet is 10 m s ⁻¹ , the minimum rate of mass flow of water required to just start the motion of the block is: (Take g = 10 m s ⁻² )

Step-by-step solution

For the block to just start moving, the force exerted by the water jet must be equal to the limiting static friction between the block and the surface. The limiting static friction f_ L is: f_ L = M g Given = 0.4 , M = 5 kg , and g = 10 m s ⁻² : f_ L = 0.4 5 10 = 20 N The force F exerted by the horizontal water jet on the block is: F = v dm dt where v = 10 m s ⁻¹ is the velocity of the jet and dm dt is the rate of mass flow of water. Equating the thrust force to the limiting friction: v dm dt = f_ L 10 dm dt = 20 d