A cylindrical tank of height `H` is open at the top end and it has a radius `r`. Water is filled in it up to a height of `h`. The time taken to empty the tank through a hole of radius `r'` in its bottom is

Options

A. `sqrt((2h)/(g))((R^(2))/(r^(2)))`
B. `sqrt((2H)/(g))((R^(2))/(r^(2)))`
C. `sqrt(h)(H)`
D. `sqrt((2H)/(g))((R)/(r))`

Answer

A

Explanation

`-piR^(2)(dh)/(dt)=pir^(2)sqrt(2gh)or(dh)/(dt)=-(r^(2))/(R^(2))sqrt(2gh)`
or `dt=-(R^(2))/(r^(2))(1)/(sqrt(2gh))dhbecauseint_(0)^(t)dt=(R_(2))/(r^(2)sqrt(2g))int_(h)^(0)h^(-1//2)dh`
or `t=-(R^(2))/(r^(2)sqrt(2g))xx2[sqrt(h)]_(h)^(0) or t=sqrt((2h)/(g))[(R^(2))/(r^(2))]`