AP EAMCET202125 Aug 2021Morning ShiftPhysicsMechanical Properties of FluidsActual
A cylindrical tank is filled with water to a level of 3 ~m . A hole is opened at a height of 52.5 ~cm from the bottom. The ratio of the area of the hole to that of the cross-sectional area of the tank is 0.1 . The square of the speed with which water will be coming out from the orifice is (g=10 ~ms ⁻² )
Options
- A50 ~m ^2 ~s ⁻²
- B40 ~m ^2 ~s ⁻²
- C51.5 ~m ^2 ~s ⁻²
- D50.5 ~m ^2 ~s ⁻²
Correct answer
A. 50 ~m ^2 ~s ⁻²
Step-by-step solution
Let a be area of hole, v_ be the velocity of efflux, h be the height of liquid above the hole. Let v be the speed with which level decreases in the container. From equation of continuity, a v_e=A v v= a v_e A Using Bernoulli's theorem, array rlrl & p₀+h g+ 1 2 v^2 & =p₀+ 1 2 v_e^2 & h g+ 1 2 ( a v_e A )^2 & = 1 2 v_e^2 or & v_e^2= 2 g h 1- ( a^2 A^2 ) & = 2 (3-0.525) 10 1-(0.1)^2 & & v_e^2 & =50 ~m ^2 ~s ⁻² array