Natural length of a spring is 60 cm and its spring constant is 4000 N/m. A mass of 20 kg is hung from it. The extension produced in the spring is (Take, `g = 9.8 m//s^(2)`)

Options

A. 4.9 cm
B. 0.49 cm
C. 9.4 cm
D. 0.94 cm

Explanation

To find the extension produced in the spring when a mass is hung from it, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Natural length of the spring, \( L = 60 \, \text{cm} \) (not directly needed for extension calculation)
- Spring constant, \( k = 4000 \, \text{N/m} \)
- Mass hung from the spring, \( m = 20 \, \text{kg} \)
- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)

2. **Calculate the Weight of the Mass:**
The weight \( W \) of the mass can be calculated using the formula:
\[ W = m \cdot g \]
Substituting the values:
\[ W = 20 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 196 \, \text{N} \]

3. **Apply Hooke's Law:**
According to Hooke's Law, the force exerted by the spring is proportional to the extension \( x \):
\[ F = k \cdot x \]
At equilibrium, the weight of the mass equals the spring force:
\[ W = k \cdot x \]
Therefore, we can set up the equation:
\[ mg = kx \]

4. **Rearranging the Equation to Solve for Extension \( x \):**
Rearranging gives us:
\[ x = \frac{mg}{k} \]

5. **Substituting the Known Values:**
Now substituting the values we calculated:
\[ x = \frac{196 \, \text{N}}{4000 \, \text{N/m}} \]

6. **Calculating the Extension:**
Performing the division:
\[ x = 0.049 \, \text{m} \]

7. **Convert to Centimeters:**
To convert meters to centimeters, multiply by 100:
\[ x = 0.049 \, \text{m} \times 100 = 4.9 \, \text{cm} \]

8. **Conclusion:**
The extension produced in the spring is \( 4.9 \, \text{cm} \).

### Final Answer:
The extension produced in the spring is **4.9 cm**.