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 analyze the buoyancy forces acting on the body when it floats in water and oil. We will use the principle of buoyancy, which states that the buoyant force is equal to the weight of the fluid displaced by the submerged part of the body.

### Step-by-Step Solution:

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

2. **Defining Variables**:
- Let \( V \) be the total volume of the body.
- Let \( \sigma_w \) be the density of water (approximately \( 1000 \, \text{kg/m}^3 \)).
- Let \( \sigma_o \) be the density of oil.
- The buoyant force \( F_b \) is equal to the weight of the fluid displaced.

3. **Buoyant Force in Water**:
- The volume submerged in water is \( 0.6V \).
- The buoyant force in water can be expressed as:
\[ F_{b,w} = \text{Volume submerged} \times \text{Density of water} \times g = 0.6V \sigma_w g \]

4. **Buoyant Force in Oil**:
- The volume submerged in oil is \( 0.4V \).
- The buoyant force in oil can be expressed as:
\[ F_{b,o} = \text{Volume submerged} \times \text{Density of oil} \times g = 0.4V \sigma_o g \]

5. **Setting Up the Equations**:
- The weight of the body is equal to the buoyant force when it is floating. Therefore:
\[ F_{b,w} = F_{b,o} \]
- This gives us the equation:
\[ 0.6V \sigma_w g = 0.4V \sigma_o g \]

6. **Cancelling Common Terms**:
- We can cancel \( V \) and \( g \) from both sides of the equation:
\[ 0.6 \sigma_w = 0.4 \sigma_o \]

7. **Rearranging the Equation**:
- Rearranging gives:
\[ \frac{\sigma_o}{\sigma_w} = \frac{0.6}{0.4} = \frac{6}{4} = \frac{3}{2} \]

8. **Finding the Relative Density of Oil**:
- The relative density (specific gravity) of oil is defined as the ratio of the density of oil to the density of water:
\[ \text{Relative Density of Oil} = \frac{\sigma_o}{\sigma_w} = \frac{3}{2} = 1.5 \]

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