JEE PYQ: Mechanical Properties Of Fluids Question 31
Question 31 - 2019 (10 Jan 2019 Shift 1)
Water flows into a large tank with flat bottom at the rate of $10^{-4}$ m$^3$ s$^{-1}$. Water is also leaking out of a hole of area 1 cm$^2$ at its bottom. If the height of the water in the tank remains steady, then this height is:
(1) 5.1 cm
(2) 7 cm
(3) 4 cm
(4) 9 cm
Show Answer
Answer: (1) 5.1 cm
Solution
Since height of water column is constant therefore, water inflow rate ($Q_{\text{in}}$) = water outflow rate $Q_{\text{in}} = 10^{-4}$ m$^3$s$^{-1}$ $Q_{\text{out}} = Au = 10^{-4} \times \sqrt{2gh}$ $\therefore 10^{-4} = 10^{-4} \times \sqrt{20 \times h}$ $\therefore h = \frac{1}{20}$ m $= 5$ cm
BETA
