Assertion : A conducting rod is placed between boiling water and ice. If rod is broken into two equal parts and two parts are connected side by side, then rate of melting of ice will increase ot four times.
Reason : Thermal resistance will become four times.

Options

A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

To solve the problem, we need to analyze the assertion and the reason provided in the question regarding the conducting rod placed between boiling water and ice.

### Step 1: Understand the Assertion
The assertion states that if a conducting rod is placed between boiling water and ice, and then the rod is broken into two equal parts and connected side by side, the rate of melting of ice will increase by four times.

### Step 2: Analyze the Heat Transfer
The rate of heat transfer (dQ/dt) through a conducting rod can be expressed using Fourier's law of heat conduction:
\[ \frac{dQ}{dt} = \frac{k \cdot A \cdot \Delta T}{L} \]
where:
- \( k \) is the thermal conductivity of the material,
- \( A \) is the cross-sectional area,
- \( \Delta T \) is the temperature difference,
- \( L \) is the length of the rod.

### Step 3: Effect of Breaking the Rod
When the rod is broken into two equal parts:
- The length of each part becomes \( L/2 \).
- When connected side by side, the effective area \( A \) doubles (i.e., \( 2A \)).

### Step 4: Calculate the New Rate of Heat Transfer
Substituting the new values into the heat transfer equation:
\[ \frac{dQ}{dt}_{new} = \frac{k \cdot (2A) \cdot \Delta T}{L/2} \]
This simplifies to:
\[ \frac{dQ}{dt}_{new} = \frac{2k \cdot A \cdot \Delta T \cdot 2}{L} = 4 \cdot \frac{k \cdot A \cdot \Delta T}{L} \]
Thus, the new rate of heat transfer is four times the original rate:
\[ \frac{dQ}{dt}_{new} = 4 \cdot \frac{dQ}{dt}_{original} \]

### Step 5: Conclusion on Melting of Ice
Since the rate of heat transfer to the ice increases by four times, the rate of melting of ice will also increase by four times. Therefore, the assertion is correct.

### Step 6: Analyze the Reason
The reason states that thermal resistance will become four times. However, thermal resistance \( R \) can be expressed as:
\[ R = \frac{L}{k \cdot A} \]
After breaking the rod:
- The new length is \( L/2 \),
- The new area is \( 2A \).

Thus, the new thermal resistance becomes:
\[ R_{new} = \frac{L/2}{k \cdot (2A)} = \frac{L}{4kA} \]
This shows that the thermal resistance actually decreases to one-fourth of the original resistance, not increases.

### Final Conclusion
- The assertion is correct: the rate of melting of ice will increase by four times.
- The reason is incorrect: thermal resistance will decrease to one-fourth, not increase.

### Answer:
- Assertion: True
- Reason: False