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.
• D. 4a - 3b

Answer 1

The correct option is B 5b - 4a

b) Let L is the original length of the wire and K is force constant of wire.

Final length=initial length+elongation

L' = 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 (i) and (ii) equation 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.