A wire fixed at the upper end stretches by length l by applying a force F. The work done in stretching is

Options

A. (a) 2Fl
B. (b) Fl
C. (c) `(F)/(2l)`
D. (d) `(Fl)/(2)`

Explanation

To find the work done in stretching a wire that is fixed at one end and stretched by a length \( L \) when a force \( F \) is applied, we can follow these steps:

### Step 1: Understand the relationship between force and extension
When a force \( F \) is applied to stretch the wire, the wire will experience an extension \( L \). The force applied is not constant; it varies from 0 to \( F \) as the wire is stretched.

### Step 2: Calculate the average force
Since the force starts from 0 and increases to \( F \), the average force \( F_{avg} \) during the stretching process can be calculated as:
\[ F_{avg} = \frac{0 + F}{2} = \frac{F}{2} \]

### Step 3: Use the work done formula
The work done \( W \) in stretching the wire can be calculated using the formula:
\[ W = F_{avg} \times L \]
Substituting the average force into the equation gives:
\[ W = \left(\frac{F}{2}\right) \times L \]

### Step 4: Final expression for work done
Thus, the work done in stretching the wire is:
\[ W = \frac{F \cdot L}{2} \]

### Conclusion
The work done in stretching the wire by a length \( L \) under the force \( F \) is given by:
\[ W = \frac{F \cdot L}{2} \]