When a load W is hung from a wire, it extends by `Deltal`. The heat produced in the process is

Options

A. `W xx Deltal`
B. `(1)/(2)Wxx Deltal`
C. `(WxxDeltal)/(4)`
D. Zero

Answer

To solve the problem of calculating the heat produced when a load \( W \) is hung from a wire that extends by \( \Delta L \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Work Done by Gravity:**
When a load \( W \) is hung from the wire, it exerts a force due to gravity. The work done by this force as the wire stretches by \( \Delta L \) can be calculated using the formula:
\[ \text{Work done by gravity} = W \times \Delta L \]

2. **Calculate the Energy Stored in the Wire:**
The energy stored in the wire due to its extension can be represented as the elastic potential energy. For a wire stretched by a force \( W \), the energy stored is given by:
\[ \text{Energy stored} = \frac{1}{2} W \times \Delta L \]

3. **Determine the Heat Produced:**
The heat produced in the process can be understood as the difference between the work done by gravity and the energy stored in the wire. Thus, we can express this as:
\[ \text{Heat produced} = \text{Work done by gravity} - \text{Energy stored} \]
Substituting the values from the previous steps:
\[ \text{Heat produced} = (W \times \Delta L) - \left(\frac{1}{2} W \times \Delta L\right) \]

4. **Simplify the Expression:**
Now, we can simplify the expression for heat produced:
\[ \text{Heat produced} = W \times \Delta L - \frac{1}{2} W \times \Delta L = \frac{1}{2} W \times \Delta L \]

5. **Final Result:**
Therefore, the heat produced when a load \( W \) is hung from a wire that extends by \( \Delta L \) is:
\[ \text{Heat produced} = \frac{1}{2} W \Delta L \]