A body floats on water and then also on an oil of densily `1.25`. Which of the following is/are true?

Options

A. The body loses more weight in oil than in water.
B. The volume of water displaced is `1.25` times that of oil diplaced
C. The body experiences equal upthrust form water and oil.
D. Apparent weight is zero in both cases.

Explanation

To solve the problem, we need to analyze the conditions under which a body floats in water and oil, and derive the implications of these conditions.

### Step-by-Step Solution:

1. **Understanding Floating Condition**:
When an object floats, the buoyant force acting on it is equal to its weight. The buoyant force is given by the formula:
\[ F_b = \rho_{liquid} \cdot g \cdot V_{submerged} \]
where \( \rho_{liquid} \) is the density of the liquid, \( g \) is the acceleration due to gravity, and \( V_{submerged} \) is the volume of the object submerged in the liquid.

2. **Case of Water**:
Let’s denote the density of water as \( \rho_{water} = 1 \, \text{g/cm}^3 \) (or \( 1000 \, \text{kg/m}^3 \)). If the weight of the body is \( W \), then:
\[ W = \rho_{water} \cdot g \cdot V_{submerged, water} \]
Rearranging gives:
\[ V_{submerged, water} = \frac{W}{\rho_{water} \cdot g} \]

3. **Case of Oil**:
For the oil with a density of \( \rho_{oil} = 1.25 \, \text{g/cm}^3 \) (or \( 1250 \, \text{kg/m}^3 \)), we have:
\[ W = \rho_{oil} \cdot g \cdot V_{submerged, oil} \]
Rearranging gives:
\[ V_{submerged, oil} = \frac{W}{\rho_{oil} \cdot g} \]

4. **Comparing Volumes Submerged**:
Since the weight \( W \) of the body remains the same in both cases, we can compare the volumes submerged:
\[ V_{submerged, water} = \frac{W}{\rho_{water} \cdot g} \quad \text{and} \quad V_{submerged, oil} = \frac{W}{\rho_{oil} \cdot g} \]
From this, we can see:
\[ V_{submerged, water} = \frac{W}{1 \cdot g} \quad \text{and} \quad V_{submerged, oil} = \frac{W}{1.25 \cdot g} \]
This implies:
\[ V_{submerged, water} = 1.25 \cdot V_{submerged, oil} \]
Therefore, the volume of water displaced is 1.25 times the volume of oil displaced.

5. **Apparent Weight**:
The apparent weight of the body when floating is zero because the buoyant force equals the weight of the body. Thus, the net force acting on the body is zero:
\[ W - F_b = 0 \quad \Rightarrow \quad W = F_b \]
Hence, the apparent weight is zero in both cases.

### Conclusion:
From the analysis, we can conclude:
- The volume of water displaced is 1.25 times the volume of oil displaced.
- The apparent weight is zero in both cases.

### True Statements:
- B: The volume of water displaced is 1.25 times the volume of oil displaced.
- C: The body experiences equal buoyant force in both cases.
- D: The apparent weight is zero in both cases.