Question

The extension in an elastic string varies directly as the weight hung on it. If a weight $250gm$ produces an extension of $3.5cm$, Find the extension produced by the weight of $700{\rm{ }}gm$?

Answer 1

Hint: Here we use the concept of direct proportion.

Complete step by step solution:
Given: The extension varies directly as the weight. The weight of $250gm$ produces an extension of $3.5cm$.

Let the quantities be termed as ${E_1},{W_{1,}},{E_2}and{\rm{ }}{W_2}$ respectively.
According to the question, quantities are in direct proportion
$\begin{array}{l}
 \Rightarrow elasticity(E) \propto weight(W)\\
 \Rightarrow \frac{{{E_1}}}{{{E_2}}} = \frac{{{W_1}}}{{{W_2}}}\\
 \Rightarrow \frac{{3.5}}{{{E_2}}} = \frac{{250}}{{700}}\\
 \Rightarrow {E_2} = \frac{{3.5 \times 700}}{{250}}\\
 \Rightarrow {E_2} = 9.8cm\\

\end{array}$

Therefore, the spring produces an extension of $9.8cm$ when a weight of $700gm$ is hung on it.

Note: In such type of questions which involves relations between the terms type of proportional is to be identified between the quantities. Accordingly, the relations are framed and assign the known values in relation to get the unknown value.