A cylinder of height 20 m is completely filled with water. The velocity of efflux of water through a hole on the side wall of the cylinder near its bottom is (Take `g=10 m s^(-2)`)

Options

A. `10 m s^(-1)`
B. `20 m s^(-1)`
C. 25.5 m `s^(-1)`
D. `5 m s^(-1)`

Explanation

To find the velocity of efflux of water through a hole in the side wall of a cylinder, we can use Torricelli's theorem, which states that the velocity of efflux (V) of a fluid under the force of gravity from an opening is given by the formula:

\[ V = \sqrt{2gh} \]

where:
- \( V \) is the velocity of efflux,
- \( g \) is the acceleration due to gravity,
- \( h \) is the height of the fluid column above the hole.

### Step-by-Step Solution:

1. **Identify the given values:**
- Height of the cylinder, \( h = 20 \, \text{m} \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)

2. **Write the formula for velocity of efflux:**
\[ V = \sqrt{2gh} \]

3. **Substitute the values into the formula:**
\[ V = \sqrt{2 \times 10 \, \text{m/s}^2 \times 20 \, \text{m}} \]

4. **Calculate the value inside the square root:**
\[ V = \sqrt{2 \times 10 \times 20} = \sqrt{400} \]

5. **Find the square root:**
\[ V = 20 \, \text{m/s} \]

### Final Answer:
The velocity of efflux of water through the hole is \( 20 \, \text{m/s} \).