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. `5b-4a`
C. `2b-(1)/(4)a`
D. `4a-3b`

Answer

B

Explanation

Let L is the original length of the wire and k is force constant of wire .
Final length= intial length + elongation
`L'=L+(F)/(k)`
For first condition ` a=L+(4)/(k) `....... (i)
For second condition `b=L+(5)/(k)` ...............(ii)
By solving Eqs. (i) and (ii) , we get
`L= 5a-4b and k=(1)/(b-a)`
Now , when the longitudinal tension is 9 N, length of the string
`L+(9)/(k)=5a-4b+9(b-a)`
`= 5b-4a`