Question

A cylindrical tank has a hole of 1 cm in its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of `70 cm//sec` . then the maximum height up to which water can rise in the tank is
A. `2.5cm`
B. `5cm`
C. `10cm`
D. `0.25cm`

Answer 1

Correct Answer - A
The height of water in the tank becomes maximum when the volume of water flowing into the tank per second becomes equal to the volume flowing out per second.
Volume of water flowing out per second `=Aupsilon =Asqrt(2gh)`
and volume of water flowing in per second `=70cm^(3)//sec`.
`therefore A sqrt(2gh) = 70 implies 1xxsqrt(2gh) = 70 implies 1xxsqrt(2xx980xxh)=70 therefore h =(4900)/(1960) = 2.5cm`.