A liquid of density ρ comes out with a velocity V from a horizontal tube of area of cross - section A fitted at the bottom of a large tank. The reaction force exerted by the liquid on the tube is F.
a) F$\propto$ V            b) F $\propto$V²              c) F$\propto$A             d) F$\propto$ρ

detailed solution

Correct option is B

Since the tank is large, velocity of liquid just before entering the pipe is zero. Rate of volume flow, Q=AV. Rate of mass flow m =ρAV. Rate of flow of momentum of the liquid just after entering the pipe, pf = mV = ρAV2. Rate of flow of momentum of liquid just before entering the pipe, pi = 0∴ Force exerted by the walls of the pipe on the liquid = pf - pi = ρAV2. By Newton's Third Law of motion, magnitude of force exerted by the liquid on the pipe = ρAV2