A body cools down from `65^(@)C` to `60^(@)C` in 5minutes. It will cool down from `60^(@)C` to `55^(@)C` in

Options

A. `5` minutes
B. less than `5` minutes
C. more than `5` minutes
D. less than or more than 5 minutes depending on whether its mass is more than or less than `1 kg`

Explanation

To solve the problem of how long it takes for a body to cool from 60°C to 55°C, we will use Newton's Law of Cooling. Here are the steps to arrive at the solution:

### Step-by-Step Solution:

1. **Identify Initial and Final Temperatures**:
- The body cools from 65°C to 60°C in 5 minutes.
- We need to find the time it takes to cool from 60°C to 55°C.

2. **Calculate Average Temperature for the First Interval**:
- The average temperature when cooling from 65°C to 60°C is:
\[ T_{avg1} = \frac{65 + 60}{2} = 62.5°C \]

3. **Determine the Temperature Difference for the First Interval**:
- Let \( T \) be the surrounding temperature. The average temperature difference for the first interval is:
\[ \Delta T_1 = T_{avg1} - T = 62.5 - T \]

4. **Apply Newton's Law of Cooling for the First Interval**:
- According to Newton's Law of Cooling, the rate of cooling is proportional to the temperature difference:
\[ \text{Rate of cooling} \propto \Delta T_1 \]
- The time taken to cool from 65°C to 60°C is given as 5 minutes.

5. **Calculate Average Temperature for the Second Interval**:
- The average temperature when cooling from 60°C to 55°C is:
\[ T_{avg2} = \frac{60 + 55}{2} = 57.5°C \]

6. **Determine the Temperature Difference for the Second Interval**:
- The average temperature difference for the second interval is:
\[ \Delta T_2 = T_{avg2} - T = 57.5 - T \]

7. **Set Up the Proportional Relationship**:
- From Newton's Law of Cooling, we can set up the ratio of the times based on the temperature differences:
\[ \frac{t_1}{t_2} = \frac{\Delta T_1}{\Delta T_2} \]
- Where \( t_1 = 5 \) minutes and \( t_2 \) is the unknown time we want to find.

8. **Substitute the Known Values**:
- Substituting the known values:
\[ \frac{5}{t_2} = \frac{62.5 - T}{57.5 - T} \]

9. **Rearranging the Equation**:
- Rearranging gives:
\[ t_2 = 5 \cdot \frac{57.5 - T}{62.5 - T} \]

10. **Analyze the Result**:
- Since \( 62.5 - T \) is greater than \( 57.5 - T \), the fraction \( \frac{57.5 - T}{62.5 - T} \) is less than 1. Therefore, \( t_2 \) will be less than 5 minutes.
- However, since the cooling rate decreases as the temperature approaches the surrounding temperature, the time taken to cool from 60°C to 55°C will be greater than 5 minutes.

### Conclusion:
The body will cool down from 60°C to 55°C in more than 5 minutes.