A rectangular block is 5 cm xx 5 cm xx 10 cm in size. The block floating in water change will occur in the level of water ?

Options

A. no change
B. it will rise
C. it will fall
D. it may rise of fall depending on the density of block

Explanation

To solve the problem of how the water level changes when a rectangular block is floating in water, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the dimensions of the block**:
The block has dimensions of 5 cm x 5 cm x 10 cm.

2. **Understand the initial orientation**:
Initially, the block is floating with its 5 cm side vertical. This means that the height of the block submerged in water is 5 cm.

3. **Calculate the volume of the block**:
The volume \( V \) of the rectangular block can be calculated using the formula for the volume of a rectangular prism:
\[ V = \text{length} \times \text{width} \times \text{height} = 5 \, \text{cm} \times 5 \, \text{cm} \times 10 \, \text{cm} = 250 \, \text{cm}^3 \]

4. **Determine the mass of the block**:
The mass \( m \) of the block can be calculated if we know its density \( \rho \). However, since the block is floating, we only need to know that the mass remains constant regardless of its orientation.

5. **Understand the principle of flotation**:
According to Archimedes' principle, the weight of the water displaced by the block is equal to the weight of the block. Since the block is floating, the volume of water displaced will remain constant as long as the mass of the block does not change.

6. **Change the orientation of the block**:
Now, the block is turned so that its 10 cm side is vertical. In this case, the height of the submerged part of the block will change.

7. **Calculate the new submerged volume**:
When the 10 cm side is vertical, the submerged height of the block will be different. However, the total volume of water displaced must remain the same because the mass of the block has not changed.

8. **Conclusion on water level change**:
Since the volume of water displaced remains constant regardless of the orientation of the block, the level of water will not change.

### Final Answer:
There will be **no change in the level of the water** when the block is turned from having its 5 cm side vertical to having its 10 cm side vertical.

---