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

Options

A. `(a+b)`
B. `(4b-5a)`
C. `(5b-4a)`
D. `(9b-9a)`

Answer

C

Explanation

(c) Let l be the natureal length and `K=(=(YA)/(l))` be the force constant of wire. Then
`a=l+(4)/(K)" "…(i)(F=K Deltal " or " Deltal=(F)/(K))`
and `b=l+(5)/(K)" "…(ii)`
On solving Eqs. (i) and (ii), we get
or `(1)/(K)=(b-a)` and `l=(5a-4b)`
Now, when T=9N
`l'=l+(9)/(K)=(5a-4b)+9(b-a)=(5b-4a)`