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

Answer

To solve the problem step by step, we will use the principle that the amount of extension in a spring is directly proportional to the weight hung on it.

### Step-by-Step Solution:

1. **Identify the given values**:
- Weight (W1) = 5 kg
- Extension (E1) = 0.4 cm

2. **Establish the relationship**:
Since the extension is proportional to the weight, we can express this relationship as:
\[ \frac{E1}{W1} = \frac{E2}{W2} \]
where \(E2\) is the new extension (5 cm) and \(W2\) is the weight we need to find.

3. **Substitute the known values**:
\[ \frac{0.4 \text{ cm}}{5 \text{ kg}} = \frac{5 \text{ cm}}{W2} \]

4. **Cross-multiply to solve for \(W2\)**:
\[ 0.4 \text{ cm} \times W2 = 5 \text{ cm} \times 5 \text{ kg} \]
\[ 0.4 W2 = 25 \]

5. **Divide both sides by 0.4 to isolate \(W2\)**:
\[ W2 = \frac{25}{0.4} \]

6. **Calculate \(W2\)**:
\[ W2 = 62.5 \text{ kg} \]

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

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