A stopper is used to block a small hole at the base of a vessel. Force exerted by liquid on stopper is F1. The stopper is then removed. Force experienced by vessel due to issuing liquid now is F2 neglect atmospheric pressure, F1/F2 =?
Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.
Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA
When the stopper blocks the hole, the force F1 is simply the hydrostatic pressure at depth h times the area A of the hole. Since pressure P = ρgh, we get F1 = ρghA.
After removal, the liquid issues out. The force F2 on the vessel is the rate of change of momentum of the issuing liquid. Using Torricelli's theorem, the speed of efflux v = √(2gh). The mass flow rate is dm/dt = ρAv. The force F2 = (dm/dt)v = ρA(2gh).
Therefore, the ratio F1/F2 = (ρghA) / (2ρghA) = 1/2.
Final Answer: