Question

The length of a rubber cord is $l_1$ metres when the tension in it is $4N$ and $l_2$ metres when the tension is $5N$. then the length in meters when the tension is $9N$ is

• A. $3l_2+4l_1$
• B. $3l_2+2l_1$
• C. $5l_2-4l_1$
• D. $3l_2-2l_1$

Answer 1

The correct option is C $5l_2-4l_1$

Let, $x_{1,}{x}_2,and{x}_{3}betheextensionwith4N,5Nand9Ntensionrespectively.4=k{x}_{1,},5=k{x}_{2}and9=k{x}_3$

Let l be the natural length of the rubber chord.

Therefore, we can say,

$x_1+l=l_1-------\left(a\right)x_2+l=l_2--------\left(b\right)x_3+l=l_3--------\left(c\right)\frac{4}{5}=\frac{x_1}{x_2}=\frac{l_1-l}{l_2-l}=>l=5l_1-4l_2-------\left(1\right)\frac{9}{5}=\frac{x_3}{x_2}=\frac{l_3-l}{l_2-l}=>9l_2-9l=5l_3-5l=>4l=9l_2-5l_{3}From\left(1\right)=>4(5l_1-4l_2)=9l_2-5l_3=>20l_1=25l_2-5l_3------\left(2\right)$

$Fromeuation(2,)l_3=5l_2-4l_1$

Therefore at 9N tension, extension is ($5l_2-4l_1$)m