Question

The length of a rubber cord is $l_{1}m$ when the tension is $4N$ and $l_{2}m$ when the tension is $6N$. The length when the tension is $9N$, is

• A. $\left(2.5l_2-1.5l_1\right)m$
• B. $\left(6l_2-1.5l_1\right)m$
• C. $\left(3l_1-2l_2\right)m$
• D. $\left(3.5l_2-2.5l_1\right)m$

Answer 1

Answer: (A)

Let the original unstretched length be $l$.
$\therefore$ $Y$ $=\frac{T}{A}$ $\frac{l}{\Delta l}$ Now $Y$ $=\frac{4}{A}$ $\frac{l}{\left(l_1-l\right)}$ $=\frac{6}{A}$ $\frac{l}{\left(l_2-l\right)}$ $=\frac{9}{A}\frac{l}{\left(l_3-l\right)}$
$\therefore$ $4\left(l_3-l\right)=9\left(l_1-l\right)$ or $4l_3+5l=9l_1$ $\dots \left(i\right)$
Again, $6\left(l_3-l\right)$ $=9\left(l_2-l\right)$or $2l_3+l=3l_2$ $\dots \left(ii\right)$
To obtain $l_3$, solve $\left(i\right)and\left(ii\right)$.
$\therefore$ $l_3$ $=\left(2.5l_2-1.5l_1\right)m$