Due to thermal expansion with rise in temperature:

Options

A. (a)metallic scale reading becames lesser that true value
B. (b)pendulum clock becomes fast
C. (c)a floating body sinks a little more
D. (d)the weight of a body in a liquid increases

Explanation

To solve the question regarding the effects of thermal expansion with a rise in temperature, we will analyze each option provided (A, B, C, D) and determine their correctness based on the principles of thermal expansion and its consequences.

### Step-by-Step Solution:

1. **Understanding Thermal Expansion**:
- When the temperature of a material increases, it typically expands. This means that the distances between particles in a solid, liquid, or gas increase.

2. **Analyzing Option A**:
- **Statement**: The distance between scales of a metallic scale will increase.
- **Explanation**: As the temperature rises, the metallic scale expands, leading to an increase in the distance between the markings on the scale. Therefore, if you measure an object using this scale, the measured value will be lower than the actual value because the scale itself has expanded.
- **Conclusion**: Option A is **correct**.

3. **Analyzing Option B**:
- **Statement**: For a pendulum clock, the time period increases with temperature.
- **Explanation**: The formula for the time period (T) of a pendulum is given by \( T = 2\pi \sqrt{\frac{L}{g}} \), where \( L \) is the length of the pendulum. As temperature increases, the length \( L \) of the pendulum increases due to thermal expansion. This results in an increase in the time period \( T \), meaning the clock runs slower.
- **Conclusion**: Option B is **incorrect** because the clock becomes slower, which is not the expected behavior.

4. **Analyzing Option C**:
- **Statement**: Due to heating, a floating body sinks less in a liquid.
- **Explanation**: When the temperature of the liquid increases, its density decreases. A floating body will sink less in a liquid with lower density compared to one with higher density. Thus, the body will float higher.
- **Conclusion**: Option C is **incorrect**.

5. **Analyzing Option D**:
- **Statement**: The apparent weight of a body in a liquid decreases due to thermal expansion.
- **Explanation**: As the volume of the body increases due to thermal expansion, the volume of water displaced also increases. According to Archimedes' principle, the buoyant force (which is equal to the weight of the displaced fluid) increases, leading to a decrease in the apparent weight of the body.
- **Conclusion**: Option D is **correct**.

### Final Summary of Options:
- **Option A**: Correct
- **Option B**: Incorrect
- **Option C**: Incorrect
- **Option D**: Correct

### Final Answer:
The correct options are A and D.

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