A tank is filled to a height H. The range of water coming out of a hole which is a depth `H//4` from the surface of water level is

Options

A. `(2H)/(sqrt(3))`
B. `(sqrt(3)H)/(2)`
C. `sqrt(3)H`
D. `(3H)/(4)`

Explanation

To solve the problem of finding the range of water coming out of a hole located at a depth of \( \frac{H}{4} \) from the surface of the water in a tank filled to a height \( H \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Depth of the Hole**:
The hole is located at a depth of \( h = \frac{H}{4} \) from the surface of the water.

2. **Determine the Height of Water Above the Hole**:
The height of water above the hole is given by:
\[ H - h = H - \frac{H}{4} = \frac{3H}{4} \]

3. **Use the Formula for Range**:
The range \( R \) of the water jet coming out of the hole can be calculated using the formula:
\[ R = 2 \sqrt{h (H - h)} \]
Substituting \( h = \frac{H}{4} \) and \( H - h = \frac{3H}{4} \):
\[ R = 2 \sqrt{\frac{H}{4} \cdot \frac{3H}{4}} \]

4. **Simplify the Expression**:
Now, simplify the expression:
\[ R = 2 \sqrt{\frac{3H^2}{16}} = 2 \cdot \frac{\sqrt{3}H}{4} = \frac{\sqrt{3}H}{2} \]

5. **Final Result**:
Therefore, the range of the water coming out of the hole is:
\[ R = \frac{\sqrt{3}H}{2} \]