The length of a spring is `alpha` when a force of `4N` is applied on it and the length is `beta` when `5N` is applied. Then the leng of spring when `9 N` force is applied is-

Options

A. 4b – 3a
B. 5b – a
C. 5b – 4a
D. 5b – 2a

Answer

C

Explanation

Let natural length of spring be `lamda_0`
Then according to question
`4=K(a-l_0)`
`5=K(b-l_0)`
`implies l_0=5a-4b, K= 1/(b-a)`
Now if we apply 9N force then
`9=K(l-l_0)implies9=(1)/((b-a))[l-5a+4b]`
`impliesl=5b-4a`