Question

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

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

Answer 1

Answer: (B)

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
$a=L+\frac{4}{k}$...(i)
For second condition
$b=L+\frac{5}{k}$...(ii)
By solving Eqs. (i) and (ii), we get
$L=5a-4b\text{ and }k=\frac{1}{b-a}$
Now, when the longitudinal tension is $9N$, length of the string
$=L+\frac{9}{k}=5a-4b+9(b-a)$
$=5b-4a$