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Question
The amount of extension in an elastic spring varies directly with the weight hung on it. If a weight of 250 gm produces an extension of 3.5 cm, find the extension produced by the weight of 700 gm.
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Solution
Let x cm be the extension produced by the weight of 700 gm.
| Weight (in gm) | 250 | 700 |
| Length (in cm) | 3.5 | x |
\[\text{ Since the amount of extension in an elastic spring varies and the weight hung on it is in direct variation, we have } : \]
\[\frac{250}{700} = \frac{3 . 5}{x}\]
\[ \Rightarrow x \times 250 = 3 . 5 \times 700\]
\[ \Rightarrow x = \frac{3 . 5 \times 700}{250}\]
\[ = \frac{2450}{250}\]
\[ = 9 . 8\]
\[\text{ Thus, the required extension will be 9 . 8 cm } .\]
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