Water of density 1000 kg/m³ is discharged horizontally from a stationary nozzle of cross-sectional area 2 cm² with speed 20 m/s. If the magnitude of the reaction force on the nozzle is N newton, find N.
Physics · Center of maas , Momentum and Collision · variable mass system
JEE Mains NEET JEE Advanced

Question

Water of density 1000 kg/m³ is discharged horizontally from a stationary nozzle of cross-sectional area 2 cm² with speed 20 m/s. If the magnitude of the reaction force on the nozzle is N newton, find N.

Physics · Center of maas , Momentum and Collision · variable mass system

G1 Physics · Accepted Answer

Convert area: A = 2 cm² = 2×10⁻⁴ m². Mass flow rate: dm/dt = ρAv = 1000×(2×10⁻⁴)×20 = 4 kg/s. The outgoing water gains horizontal momentum at the rate F(on water) = (dm/dt)v = 4×20 = 80 N. By Newton's third law, the water exerts an equal and opposite force of magnitude 80 N on the nozzle. Hence N = 80.