A horizontal jet of water coming out of a pipe of area of cross-section 20cm2 hits a vertical wall

Q: A horizontal jet of water coming out of a pipe of area of cross-section 20 cm2 hits a vertical wall with a velocity of 10 m/s and rebounds with the same speed. The force exerted by water on the wall is,(Density of water = 1000 kg/m3)

(a) 0.2 N

(b) 10N

(c) 400 N

(d) 200 N

Ans: (c)

Sol: Volume per sec = A v ; Where A = area of cross-section

Mass per sec = A v ρ ; Where ρ = density

Momentum per sec = (A v ρ)v = A v2 ρ

Force exerted = Change in Momentum per sec

F = 2 A v2 ρ (Since , rebounding)

F = 2 × (20 × 10-4)× (10)2 ×1000

F = 400 N