Any solid will not sink in water if its relative density is

Options

A. less than 1
B. equal to 1
C. greater than 1
D. infinite

Answer

To determine under what conditions a solid will not sink in water, we need to consider the concept of relative density (or specific gravity) and how it relates to the density of water.

### Step-by-Step Solution:

1. **Understanding Relative Density**:
Relative density is defined as the ratio of the density of a substance to the density of a reference substance, usually water. The formula for relative density (RD) is:
\[ RD = \frac{\text{Density of the solid}}{\text{Density of water}} \]

2. **Density of Water**:
The density of water is approximately \(1 \, \text{g/cm}^3\) at standard conditions.

3. **Condition for Floating**:
A solid will float in water if its density is less than that of water. This means:
\[ \text{Density of the solid} < \text{Density of water} \]
In terms of relative density, this condition can be expressed as:
\[ RD < 1 \]

4. **Evaluating the Options**:
- **Option 1**: Less than 1 (Correct)
- **Option 2**: Equal to 1 (The solid will be neutrally buoyant, meaning it will neither sink nor float but stay suspended)
- **Option 3**: Greater than 1 (The solid will sink)
- **Option 4**: Not specified

5. **Conclusion**:
From the analysis, we conclude that any solid will not sink in water if its relative density is less than 1.

Thus, the answer is **Option 1: Less than 1**.