A body floats in water with 40% of its volume outside water. When the same body floats in an oil. 60% of its volume remians outside oil. The relative density of oil is

Options

A. `0.9`
B. `1.0`
C. `1.2`
D. `1.5`

Explanation

To solve the problem, we need to use the principle of buoyancy, which states that the weight of the fluid displaced by a floating body is equal to the weight of the body itself.

### Step-by-step Solution:

1. **Understanding the Problem**:
- The body floats in water with 40% of its volume above the water surface. This means that 60% of its volume is submerged in water.
- When the body floats in oil, 60% of its volume is above the oil surface, meaning that 40% of its volume is submerged in oil.

2. **Setting Up the Equations**:
- Let \( V \) be the total volume of the body.
- The density of water is \( \rho_1 \) (approximately \( 1000 \, \text{kg/m}^3 \)).
- The density of oil is \( \rho_2 \).
- The volume submerged in water is \( 0.6V \) and the volume submerged in oil is \( 0.4V \).

3. **Applying the Principle of Buoyancy**:
- The weight of the body is equal to the weight of the water displaced:
\[ \text{Weight of body} = \text{Weight of water displaced} \]
\[ mg = (0.6V) \rho_1 g \]
- The weight of the body can also be expressed in terms of its density \( \sigma_1 \) (density of the body):
\[ mg = V \sigma_1 g \]
- Equating the two expressions:
\[ V \sigma_1 g = (0.6V) \rho_1 g \]
- Canceling \( Vg \) from both sides:
\[ \sigma_1 = 0.6 \rho_1 \]

4. **For the Oil**:
- Similarly, for the oil:
\[ mg = (0.4V) \rho_2 g \]
- Again, equating the weight of the body:
\[ V \sigma_1 g = (0.4V) \rho_2 g \]
- Canceling \( Vg \):
\[ \sigma_1 = 0.4 \rho_2 \]

5. **Relating the Densities**:
- Now we have two equations for \( \sigma_1 \):
\[ 0.6 \rho_1 = 0.4 \rho_2 \]
- Rearranging gives:
\[ \frac{\rho_2}{\rho_1} = \frac{0.6}{0.4} = 1.5 \]

6. **Finding the Relative Density of Oil**:
- The relative density of oil is defined as:
\[ \text{Relative Density of Oil} = \frac{\rho_2}{\rho_1} \]
- From our calculation, we find:
\[ \text{Relative Density of Oil} = 1.5 \]

### Final Answer:
The relative density of oil is **1.5**.