A large tank filled with water to a height `h` is to be emptied through a small hole at the bottom. The ratio of times taken for the level of water to fall from h to `(h)/(2)` and from `(h)/(2)` to zero is

Options

A. `sqrt(2)`
B. `(1)/(sqrt(2))`
C. `sqrt(2)-1`
D. `(1)/(sqrt(2)-1)`

Explanation

To solve the problem of finding the ratio of times taken for the water level to fall from height \( h \) to \( \frac{h}{2} \) and from \( \frac{h}{2} \) to \( 0 \), we can use Torricelli's law and integrate to find the time taken for each segment.

### Step-by-Step Solution:

1. **Understanding the Problem:**
- We have a tank filled with water to a height \( h \).
- Water is draining through a small hole at the bottom.
- We need to find the ratio of time taken for the water level to fall from \( h \) to \( \frac{h}{2} \) (let's call this time \( T_1 \)) and from \( \frac{h}{2} \) to \( 0 \) (let's call this time \( T_2 \)).
...