Two test tubes A and B of same mass with equal areas of cross-section are used as variable immersion hydrometer. If the length of test tube 'A' is double that of 'B', then the range of densities that can be measured by 'A' is

Options

A. more than the range of densities that can be measured using 'B'.
B. less than the range of densities that can be measured wing 'B'.
C. equal to the range of densities that can be measured using 'B'.
D. Both (b) and (c).

Explanation

To solve the problem, we need to analyze the relationship between the length of the test tubes and the range of densities that can be measured by them.

### Step-by-Step Solution:

1. **Understanding the Concept of a Hydrometer**:
A hydrometer measures the density of liquids. It works on the principle of buoyancy, where the amount of the hydrometer submerged in the liquid is inversely proportional to the density of the liquid.

2. **Identifying the Given Information**:
- Test tube A has a length that is double that of test tube B.
- Both test tubes have the same mass and equal areas of cross-section.

3. **Analyzing the Effect of Length on Density Measurement**:
- The range of densities that can be measured by a hydrometer is influenced by its length. A longer hydrometer can displace more liquid, allowing it to measure a wider range of densities.
- Since the length of test tube A is double that of test tube B, it can displace more liquid when immersed.

4. **Determining the Range of Densities**:
- If we denote the range of densities that can be measured by test tube B as \( R_B \), then the range of densities that can be measured by test tube A, denoted as \( R_A \), will be greater.
- Specifically, since the length of A is double that of B, the range of densities that can be measured by A will be double that of B. Thus, we can express this as:
\[ R_A = 2 \times R_B \]

5. **Conclusion**:
- Therefore, the range of densities that can be measured by test tube A is greater than that of test tube B.

### Final Answer:
The range of densities that can be measured by test tube A is double that of test tube B.