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

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. 10min

I got this question in an online interview.

The question is from Fluids Mechanical Properties in section Mechanical Properties of Fluids of Physics – Class 11

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.