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 the 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 the original length of elastic string is L and its force constant is k. When longitudinal tension 4N is applied on it
$L+\frac{5}{K}=a$ $\cdots$ (i)
and when longitudinal tension 5N is applied on it
$L+\frac{5}{K}=b$ $\cdots$ (ii)
By solving (i) and (ii) we get $k=\frac{1}{b-a}andL=5a-4b$
Now when longitudinal tension 9N is applied on elastic string then its length
$=L+\frac{9}{K}=5a-4b+9(b-a)=5b-4a$