A U-tube is partially filled with water. Oil which does not mix with water is next poured into one side, until water rises by 25 cm on the other side. If the density of oil `0.8g//cm^(3)`. The oil level will stand higher than the water by

Options

A. `6.25cm`
B. `12.50cm`
C. `31.75 cm`
D. `25 cm`

Explanation

To solve the problem, we need to analyze the U-tube filled with water and oil. We will use the principle of hydrostatic pressure, which states that the pressure at a given depth in a fluid is the same regardless of the fluid type, as long as the points are at the same horizontal level.

### Step-by-Step Solution:

1. **Understand the Setup**:
- We have a U-tube partially filled with water.
- Oil is poured into one side of the U-tube, causing the water level to rise by 25 cm on the other side.

2. **Define Variables**:
- Let the density of water be \( \rho_w = 1 \, \text{g/cm}^3 \) (or \( 1000 \, \text{kg/m}^3 \)).
- Let the density of oil be \( \rho_o = 0.8 \, \text{g/cm}^3 \) (or \( 800 \, \text{kg/m}^3 \)).
- Let the height of the oil column be \( h \).

3. **Apply Hydrostatic Pressure Principle**:
- At the level where the oil and water meet, the pressure exerted by the oil column must equal the pressure exerted by the water column on the other side.
- The pressure due to the oil column is given by:
\[ P_{\text{oil}} = \rho_o \cdot g \cdot h \]
- The pressure due to the water column (after rising by 25 cm) is:
\[ P_{\text{water}} = \rho_w \cdot g \cdot (25 \, \text{cm}) \]

4. **Set the Pressures Equal**:
- Since the pressures must balance at the same horizontal level, we have:
\[ \rho_o \cdot g \cdot h = \rho_w \cdot g \cdot 25 \]
- Note that \( g \) cancels out from both sides:
\[ \rho_o \cdot h = \rho_w \cdot 25 \]

5. **Substitute the Known Densities**:
- Substitute the values of \( \rho_o \) and \( \rho_w \):
\[ 0.8 \cdot h = 1 \cdot 25 \]

6. **Solve for \( h \)**:
- Rearranging gives:
\[ h = \frac{25}{0.8} = 31.25 \, \text{cm} \]

7. **Find the Height Difference**:
- Since the oil level stands higher than the water, we need to find the difference in height:
\[ \text{Height difference} = h - 25 \, \text{cm} = 31.25 \, \text{cm} - 25 \, \text{cm} = 6.25 \, \text{cm} \]

### Final Answer:
The oil level will stand higher than the water by **6.25 cm**.