The extension in an elastic string varies directly as the weight hung on it. If a weight of 150 g produces an extension of 2.8 cm.What weight would produce an extension of 19.6 cm?

Answer

To solve the problem step by step, we will use the concept of direct variation.

### Step 1: Understand the relationship
We know that the extension in the elastic string varies directly with the weight hung on it. This means that if we know the extension produced by a certain weight, we can find the weight needed for any other extension.

### Step 2: Establish the known values
From the problem, we know:
- Weight (W1) = 150 grams
- Extension (E1) = 2.8 cm

### Step 3: Find the weight per cm of extension
To find how much weight corresponds to 1 cm of extension, we can divide the weight by the extension:
\[ \text{Weight per cm} = \frac{W1}{E1} = \frac{150 \text{ grams}}{2.8 \text{ cm}} \]

### Step 4: Calculate weight per cm
Now, we perform the calculation:
\[ \text{Weight per cm} = \frac{150}{2.8} \approx 53.57 \text{ grams/cm} \]

### Step 5: Find the weight for the new extension
Now we need to find the weight (W2) that would produce an extension of 19.6 cm. We can use the weight per cm we calculated:
\[ W2 = \text{Weight per cm} \times \text{New Extension} \]
\[ W2 = 53.57 \text{ grams/cm} \times 19.6 \text{ cm} \]

### Step 6: Calculate the weight for 19.6 cm
Now, we perform the multiplication:
\[ W2 \approx 53.57 \times 19.6 \approx 1050 \text{ grams} \]

### Conclusion
Thus, the weight that would produce an extension of 19.6 cm is approximately **1050 grams**.

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