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. none of these

Answer

A

Explanation

`-pir^(2)(dh)/(dt)=pir^(2)sqrt(2gh)` or `(dh)/(dg)=-(r^('2))/(r^(2)) sqrt(2gh)`
or `dt=-(r^(2))/(r^('2)) 1/sqrt((2gh))dh`
`:. int_(0)^tdt=-(r^(2))/(r^('2)sqrt(2g)) int_(h)^(0)h^(-1/2)dh`
or `t=-(r^(2))/(r^('2)sqrt(2g))xx2[sqrth]_(h)^(0)` or `t=sqrt((2h)/g), (r^(2))/(r^('2))`