A rod AB is 1m long. The temperature of its one end A is maintained at `100^(@)`C and other end B at `10^(@)`C, the temperature at a distance of 60 cm from point B is

Options

A. `64^(@)`C
B. `36^(@)`C
C. `46^(@)`C
D. `72^(@)`C

Explanation

To find the temperature at a distance of 60 cm from point B in a rod AB that is 1 meter long, with one end A at 100°C and the other end B at 10°C, we can use the concept of linear temperature distribution in a uniform rod.

### Step-by-Step Solution:

1. **Identify the Lengths and Temperatures**:
- Length of the rod (AB) = 1 m = 100 cm
- Temperature at end A (T_A) = 100°C
- Temperature at end B (T_B) = 10°C
- Distance from point B to point C (where we need to find the temperature) = 60 cm

2. **Calculate the Distance from Point A**:
- Since the total length of the rod is 100 cm, the distance from point A to point C (T_C) is:
\[ \text{Distance from A to C} = \text{Total length} - \text{Distance from B to C} = 100 \text{ cm} - 60 \text{ cm} = 40 \text{ cm} \]

3. **Use the Formula for Temperature Distribution**:
- The temperature at any point in a uniform rod can be calculated using the formula:
\[ T(x) = T_A + \left( \frac{T_B - T_A}{L} \right) \cdot x \]
- Where:
- \( T(x) \) = temperature at distance \( x \) from point A
- \( T_A \) = temperature at point A
- \( T_B \) = temperature at point B
- \( L \) = total length of the rod
- \( x \) = distance from point A

4. **Substitute the Values**:
- Here, \( T_A = 100°C \), \( T_B = 10°C \), \( L = 100 \text{ cm} \), and \( x = 40 \text{ cm} \):
\[ T(40) = 100 + \left( \frac{10 - 100}{100} \right) \cdot 40 \]
\[ T(40) = 100 + \left( \frac{-90}{100} \right) \cdot 40 \]
\[ T(40) = 100 - 36 = 64°C \]

5. **Conclusion**:
- The temperature at a distance of 60 cm from point B (or 40 cm from point A) is **64°C**.