When a load of 5kg is hung on a wire then extension of 30 cm take place then work done will be :-

Options

A. 7.5 J
B. 15 J
C. 0.5 J
D. 1.5 J

Answer

To solve the problem of calculating the work done when a load of 5 kg is hung on a wire that extends by 30 cm, we can follow these steps:

### Step 1: Understand the Problem
We need to find the work done when a load is applied to a wire, causing it to extend. The work done on the wire can be calculated using the formula for elastic potential energy.

### Step 2: Identify the Given Values
- Mass of the load (m) = 5 kg
- Extension of the wire (ΔL) = 30 cm = 0.3 m (convert cm to m)
- Acceleration due to gravity (g) = 9.8 m/s² (standard value)

### Step 3: Calculate the Force
The force (F) exerted by the load due to gravity can be calculated using the formula:
\[ F = m \cdot g \]
Substituting the values:
\[ F = 5 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 49 \, \text{N} \]

### Step 4: Calculate the Work Done
The work done (W) on the wire when it is stretched can be calculated using the formula for elastic potential energy:
\[ W = \frac{1}{2} \cdot F \cdot \Delta L \]
Substituting the values:
\[ W = \frac{1}{2} \cdot 49 \, \text{N} \cdot 0.3 \, \text{m} \]
\[ W = \frac{1}{2} \cdot 49 \cdot 0.3 = \frac{49 \cdot 0.3}{2} = \frac{14.7}{2} = 7.35 \, \text{J} \]

### Step 5: Round the Result
Since the question may require a rounded answer, we can round 7.35 J to 7.5 J for simplicity.

### Final Answer
The work done when a load of 5 kg is hung on the wire causing it to extend by 30 cm is approximately **7.5 Joules**.

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