Question

The length of an elastic string is $Xm$ when the tension is $8N$, and $Ym$ when the tension is $10N$. The length in metres when the tension is $18N$ is

• A. $4X-5Y$
• B. $5Y-4X$
• C. $9X-4Y$
• D. $4Y-9X$

Answer 1

The correct option is B $5Y-4X$

Let the untstretched length of string be L.

from hook ens law,

$F=k\Delta x$ $\left[\begin{array}{c}F=Tensionapplied\\ \Delta x:Elongationofstring\Delta x:\end{array}\right]$

So, from given,

$8=k(x-l)$ $Lo=k(Y-L)$ $\to \left(1\right)$

Taking Ratio,

$\frac{X-L}{Y-L}=\frac{4}{5}\Rightarrow L=5X-4Y.$ $\to \left(2\right)$

Substitution $\left(2\right)in\left(1\right)$,

$8=K(X-(5X-4Y\left)\right)\Rightarrow K=\frac{2}{Y-X}$

So when tension $F=18n$, the length is L'(say), $\to$

$18=K(L^{\prime }-L)$

$\Rightarrow 18=\frac{2}{Y-X}\left(L^{\prime }\right(5X-4Y\left)\right)$

$\Rightarrow L^{\prime }=5Y-4X$