Statement I: The bulb of one thermometer is spherical while that of the other is cylindrical . Both have equal amounts of mercury. The response of the cylindrical bulb thermometer will be quicker.
Statement II: Heat conduction in a body is directly proportional to cross-sectional area.

Options

A. Statement -`1` is True , Statement -`2` is True , Statement -`2` is correct explanation for Statement - `1`
B. Statement -`1` is True , Statement -`2` is True , Statement -`2` is not correct explanation for Statement - `1`
C. Statement -`1` is True , Statement -`2` is False.
D. Statement -`1` is False , Statement -`2` is True.

Answer

To analyze the statements provided in the question, we will break down the reasoning step by step.

### Step 1: Understanding the Thermometer Bulbs
- The first statement mentions two thermometers: one with a spherical bulb and the other with a cylindrical bulb, both containing equal amounts of mercury.
- The shape of the bulb affects how quickly the thermometer can respond to temperature changes.

**Hint:** Consider how the shape of the bulb influences the surface area and heat transfer.

### Step 2: Analyzing Heat Transfer
- Heat conduction in a body is indeed directly proportional to the cross-sectional area. This means that a larger surface area allows for more heat to be transferred in a given time.
- The formula for heat conduction can be expressed as \( \frac{dq}{dt} = K \cdot A \cdot \frac{\Delta T}{d} \), where \( A \) is the cross-sectional area, \( K \) is the thermal conductivity, \( \Delta T \) is the temperature difference, and \( d \) is the thickness.

**Hint:** Recall the relationship between surface area and heat transfer.

### Step 3: Comparing Surface Areas
- For the same volume of liquid (mercury), a cylindrical bulb will have a larger surface area compared to a spherical bulb. This is because a sphere has the least surface area for a given volume.
- Therefore, the cylindrical thermometer will have more area exposed to the surrounding environment, allowing it to absorb heat more quickly.

**Hint:** Think about why raindrops are spherical and how that relates to surface area.

### Step 4: Conclusion on Statement I
- Since the cylindrical bulb has a larger surface area, it will respond more quickly to temperature changes compared to the spherical bulb.
- Thus, Statement I is true.

### Step 5: Conclusion on Statement II
- Statement II asserts that heat conduction is directly proportional to cross-sectional area, which is correct as per the principles of heat transfer.
- Therefore, Statement II is also true.

### Final Conclusion
- Both statements are true, and Statement I is justified by the reasoning provided in Statement II.

**Final Answer:** Both Statement I and Statement II are true.