The amount of extension in a spring is proportional to the weight hung on it. If the weight of 5 kgs produces an extension of 0.4 cm, what weight would produce an extension of 5 cm ?

Options

A. A)6.25 kgs
B. B)62.5 kgs
C. C)4 kgs.
D. D)40 kgs

Answer

To solve the problem, we will use the concept of direct proportionality between the weight hung on the spring and the extension produced in the spring.

### Step-by-Step Solution:

1. **Understand the relationship**: The problem states that the amount of extension \( e \) in a spring is proportional to the weight \( W \) hung on it. This can be expressed mathematically as:
\[ W \propto e \]
or
\[ W = k \cdot e \]
where \( k \) is a constant of proportionality.

2. **Set up the known values**: We know that when a weight of 5 kg is hung on the spring, it produces an extension of 0.4 cm. We can denote these values as:
- \( W_1 = 5 \) kg
- \( e_1 = 0.4 \) cm

3. **Set up the unknown values**: We want to find the weight \( W_2 \) that produces an extension of 5 cm. We denote these values as:
- \( e_2 = 5 \) cm
- \( W_2 = ? \)

4. **Use the proportionality relationship**: From the proportionality, we can set up the ratio:
\[ \frac{W_1}{W_2} = \frac{e_1}{e_2} \]

5. **Substitute the known values into the ratio**:
\[ \frac{5}{W_2} = \frac{0.4}{5} \]

6. **Cross-multiply to solve for \( W_2 \)**:
\[ 5 \cdot 5 = 0.4 \cdot W_2 \]
\[ 25 = 0.4 \cdot W_2 \]

7. **Isolate \( W_2 \)**:
\[ W_2 = \frac{25}{0.4} \]

8. **Calculate \( W_2 \)**:
\[ W_2 = \frac{25 \times 10}{4} = \frac{250}{4} = 62.5 \text{ kg} \]

### Final Answer:
The weight that would produce an extension of 5 cm is **62.5 kg**.