Water is drained from a vertical cylindrical tank by opening a value at the base of the tank. It is known that the rate at which the water level drops is proportional to the square root of water depth y, where the constant of proprortionality `kgt0` depends on the acceliration due to gravity and the geomety of the hole. If is measured in minutes and `k=(1)/(15)` then the time of drain the tank, If the water is 4 m deep to start with is

Options

A. 30 min
B. 45 min
C. 60 min
D. 80 min

Answer

C

Explanation

According to the question,
`(dv)/(dt)=-ksqrt(y)`
or `int_(4)^(0)(dy)/sqrt(y) =-kint_(0)^(t)dt`
or `2sqrt(y)|-(4)^(0)|=-kt =-t/15`
or `0-4=-t/15`
or t=60min