Question

The length of an elastic string is $a$ metre when the longitudinal tension is $4$N and $b$ metre when the longitudinal tension is $5$N. The length of the string in metre when longitudinal tension is $9$N is :

• A. $a-b$
• B. $5b-4a$
• C. $2b-\frac{1}{4}a$
• D. $4a-3b$

Answer 1

The correct option is B $5b-4a$

Let L is the original length of the wire and k is force constant of wire.
Final length $=$ initial length $+$ elongation
$L^{\prime }=L+\frac{F}{k}$
For first condition $a=L+\frac{4}{k}$ .....$\left(i\right)$
For second condition $b=L+\frac{5}{k}$ ......$\left(ii\right)$
By solving Eqs. $\left(i\right)$ and $\left(ii\right)$, we get
$L=5a-4b$ and $k=\frac{1}{b-a}$
Now, when the longitudinal tension is $9N$. length of the string.
$=L+\frac{9}{k}=5a-4b+9(b-a)$
$=5b-4a$