A uniform chain of length 2 m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work done in pulling the entire chain on the table?

Options

A. 7.2 J
B. 3.6 J
C. 120 J
D. 1200 J

Explanation

To solve the problem of calculating the work done in pulling the entire chain onto the table, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Length of the chain, \( L = 2 \, \text{m} \)
- Length of the chain hanging off the table, \( l = 60 \, \text{cm} = 0.6 \, \text{m} \)
- Total mass of the chain, \( M = 4 \, \text{kg} \)

2. **Calculate the Mass per Unit Length of the Chain:**
\[ \text{Mass per unit length} = \frac{M}{L} = \frac{4 \, \text{kg}}{2 \, \text{m}} = 2 \, \text{kg/m} \]

3. **Calculate the Mass of the Hanging Portion of the Chain:**
\[ \text{Mass of the hanging part} = \text{mass per unit length} \times \text{length of the hanging part} = 2 \, \text{kg/m} \times 0.6 \, \text{m} = 1.2 \, \text{kg} \]

4. **Determine the Height of the Center of Mass of the Hanging Chain:**
- The center of mass of the hanging portion (0.6 m) is located at half its length:
\[ \text{Height of the center of mass} = \frac{0.6 \, \text{m}}{2} = 0.3 \, \text{m} \]

5. **Calculate the Work Done to Raise the Center of Mass:**
- The work done \( W \) against gravity to raise the center of mass is given by:
\[ W = mgh \]
where:
- \( m = 1.2 \, \text{kg} \) (mass of the hanging part)
- \( g = 9.81 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( h = 0.3 \, \text{m} \) (height to which the center of mass is raised)

Plugging in the values:
\[ W = 1.2 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 0.3 \, \text{m} \]
\[ W = 1.2 \times 9.81 \times 0.3 = 3.5292 \, \text{J} \]

6. **Final Result:**
- Rounding to two decimal places, the work done is approximately:
\[ W \approx 3.53 \, \text{J} \]

### Conclusion:
The work done in pulling the entire chain onto the table is approximately **3.53 Joules**.