A tank filled with fresh water has a hole in its bottom and water is flowing out of it. If the size of the hole is increased, then

Options

A. the volume of water flowing out per second will decrease
B. the velocity of outflow of water remains unchanged
C. the volume of water volume out per second remains zero
D. Both (b) and (c)

Explanation

To solve the problem, we need to analyze the situation of water flowing out of a hole in the bottom of a tank as the size of the hole is increased. We will use principles from fluid mechanics, particularly Torricelli's law, which relates the speed of fluid flowing out of an orifice to the height of the fluid above it.

### Step-by-Step Solution:

1. **Understanding the Situation**:
- We have a tank filled with fresh water, and there is a hole at the bottom through which water is flowing out.

2. **Effect of Increasing the Hole Size**:
- When the size of the hole is increased, the area of the hole (A) becomes larger.

3. **Volume Flow Rate**:
- The volume flow rate (Q) of water out of the hole can be expressed as:
\[ Q = A \cdot v \]
where \( v \) is the velocity of the water flowing out.

4. **Velocity of Outflow**:
- According to Torricelli's theorem, the velocity \( v \) of the water flowing out of the hole is given by:
\[ v = \sqrt{2gh} \]
where \( g \) is the acceleration due to gravity and \( h \) is the height of the water column above the hole.

5. **Analyzing the Changes**:
- If the size of the hole increases, the area \( A \) increases. Since the velocity \( v \) is determined by the height \( h \) of the water and not by the area of the hole, the velocity remains unchanged as long as the height of the water does not change significantly.
- Therefore, if the area increases, the volume flow rate \( Q \) will increase because \( Q \) is directly proportional to the area \( A \).

6. **Conclusion**:
- As the size of the hole increases, the volume of water flowing out per second will **increase**. The velocity of outflow of water remains **unchanged** as it is dependent on the height of the water column. The statement that the volume of water output per second remains zero is incorrect.

### Final Answer:
- The volume of water flowing out per second will **increase** when the size of the hole is increased, while the velocity of outflow remains **unchanged**.