The surface of water in a water tank of cross-section area 750 cm ^2 on the top of a house is h m above the tap level. The speed of water coming out through the tap of cross-section area 500 mm ^2 is 30 cm/s. At that instant, dh/dt is y 10⁻³ m/s. The value of y will be

Step-by-step solution

By the equation of continuity, A₁ v₁ = A₂ v₂ . Here, A₁ = 750 cm ^2 , A₂ = 500 mm ^2 = 5 cm ^2 , and v₂ = 30 cm/s . Substituting the values, 750 v₁ = 5 30 . v₁ = 150 750 = 0.2 cm/s . Converting to m/s, v₁ = 0.2 10⁻² m/s = 2 10⁻³ m/s . Since v₁ = dh dt , we have dh dt = 2 10⁻³ m/s . Comparing with y 10⁻³ m/s , we get y = 2 . Answer: 2