Question

The length of a rubber cord is ${{l}_{1}}$ metre when the tension is $4\, N$ and ${{l}_{2}}$ metre when the tension is $6\, N$ . The length when the tension is $9\,N$, is

• A. $(2.5{{l}_{2}}-1.5{{l}_{1}})m$
• B. $(6{{l}_{2}}-1.5{{l}_{1}})m$
• C. $(3{{l}_{2}}-2{{l}_{1}})m$
• D. $(3.5{{l}_{2}}-2.5{{l}_{1}})m$

Answer 1

Answer: (A)

$(2.5{{l}_{2}}-1.5{{l}_{1}})m$

Answer 2

Let the original unstretched length be $l.$
$Y=\frac{Stress}{Strain}=\frac{T/A}{\Delta l/l}=\frac{T}{A}\times \frac{l}{\Delta l}$
Now $Y=\frac{4}{A}\frac{l}{({{l}_{1}}-l)}=\frac{6}{A}\frac{l}{({{l}_{2}}-l)}$
$=\frac{9}{A}\frac{l}{({{l}_{3}}-l)}$
$\therefore$ $4({{l}_{3}}-l)=9({{l}_{1}}-l)$
$\Rightarrow$ $4{{l}_{3}}+5l=9{{l}_{1}}$ .... (i)
Again, $6({{l}_{3}}-l)=9({{l}_{2}}-l)$
$\Rightarrow$ $2{{l}_{3}}+l=3{{l}_{2}}$ ...(ii)
Solve Eqs. (i) and (ii), we obtain
${{l}_{3}}=(2.5{{l}_{2}}-1.5{{l}_{1}})$