A cylindrical vessel open at the top is `20cm` high and `10 cm` in diameter. A circular hole of cross-sectional area `1cm^(2)` is cut at the centre of the bottom of the vessel. Water flows from a tube above it into the vessel at the rate of `10^(2)cm^(3)//s`. The height of water in the vessel under steady state is (Take `g=10m//s^(2))`.

Options

A. `20cm`
B. `15cm`
C. `10cm`
D. `5cm`

Answer

D

Explanation

In steady state,
Volume flow rate entering the vessel
=volume flow rate leaving the vessel
`:. Q=av=a sqrt(2gh)` or `h=(Q^(2))/(2ga^(2))`
`=((10^2)^(2))/((2xx1000)(1)^(2))=5cm`.