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.
Solution:
Let x cm be the extension produced by the weight of 700 gm.
Since the amount of extension in an elastic spring varies and the weight hung on it is in direct variation, we have :
$\frac{250}{700}=\frac{3.5}{x}$
$\Rightarrow x \times 250=3.5 \times 700$
$\Rightarrow x=\frac{3.5 \times 700}{250}$
$=\frac{2450}{250}$
$=9.8$
Thus, the required extension will be $9.8 \mathrm{~cm}$.