Question

The length of an elastic string is ametres when the longitudinal tension is 4 N and bmetres when the longitudinal tension is 5 N. The length of the string in metres 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

Answer: (B)

5b – 4a

Answer 2

Let the original length of elastic string is L and its force constant is k. When longitudinal tension 4N is applied on it $L + \frac{4}{k} = a$ .....(i)

and when longitudinal tension 5N is applied on it

$L + \frac{5}{k} = b$ .....(ii)

By solving (i) and (ii) we get $k = \frac{1}{b - a}$ and $L = 5a - 4b$

Now when longitudinal tension 9N is applied on elastic string then its length = $L + \frac{9}{k} = 5a - 4b + 9(b - a) = 5b - 4a$