A solid piece weighs 200 g in air, 150 g in water and 100 g in a liquid. The relative density of the liquid will be

Options

A. 2
B. 3
C. 4
D. 5

Explanation

To find the relative density of the liquid, we can use the following formula:

\[ \text{Relative Density} = \frac{\text{Weight of solid in air} - \text{Weight of solid in liquid}}{\text{Weight of solid in air} - \text{Weight of solid in water}} \]

### Step-by-Step Solution:

1. **Identify the weights given:**
- Weight of solid in air (W_air) = 200 g
- Weight of solid in water (W_water) = 150 g
- Weight of solid in liquid (W_liquid) = 100 g

2. **Calculate the buoyant force in the liquid:**
- Buoyant force in the liquid = Weight of solid in air - Weight of solid in liquid
\[ \text{Buoyant force in liquid} = W_{air} - W_{liquid} = 200 \, \text{g} - 100 \, \text{g} = 100 \, \text{g} \]

3. **Calculate the buoyant force in water:**
- Buoyant force in water = Weight of solid in air - Weight of solid in water
\[ \text{Buoyant force in water} = W_{air} - W_{water} = 200 \, \text{g} - 150 \, \text{g} = 50 \, \text{g} \]

4. **Substitute the values into the relative density formula:**
\[ \text{Relative Density} = \frac{100 \, \text{g}}{50 \, \text{g}} = 2 \]

5. **Conclusion:**
The relative density of the liquid is 2.

### Final Answer:
The relative density of the liquid is **2**.