A cylindrical tank of area 5m^2 contains water filled to a height of 10cm. A hole of area 0.005m^2 is present at the bottom. What is the time required for the water level to become half?(a) 100s(b) 10s(c) 1min(d) 10minI got this question in an online interview.The question is from Fluids Mechanical Properties in section Mechanical Properties of Fluids of Physics – Class 11

A cylindrical tank of area 5m^2 contains water filled to a height of 1

1.	A cylindrical tank of area 5m^2 contains water filled to a height of 10cm. A hole of area 0.005m^2 is present at the bottom. What is the time required for the water level to become half?(a) 100s(b) 10s(c) 1min(d) 10minI got this question in an online interview.The question is from Fluids Mechanical Properties in section Mechanical Properties of Fluids of Physics – Class 11
Answer» RIGHT option is (a) 100s Explanation: The speed of efflux when height of WATER is ’H’ = \(\SQRT{2gh}\).The volume of water flowing out in TIME dt is Avdt = 0.005\(\sqrt{2gh}\)dt.Therefore the decrease in height of water level (dh) in time dt is vol flowing out / area of tank= 0.005\(\sqrt{2gh}\)dt/5. dh = \(\sqrt{2gh}\) (0.005)dt/5 \(\int_{0}^{0.05}dh/\sqrt{h} = \int_{0}^{t}\sqrt{2g}\)0.001 dt ∴ 2\(\sqrt{0.05}\) = \(\sqrt{20}\)0.001 t ∴ t = \(\sqrt{0.2}\)*1000/\(\sqrt{20}\) = 100s.

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