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.

Answer 1

Let x cm be the extension produced by the weight of 700 gm.

Weight (in gm)	250	700
Length (in cm)	3.5	x

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