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. `5beta-4alpha`
B. `beta-alpha`
C. `5alpha-4beta`
D. `9(beta-alpha)`

Answer

B

Explanation

Let l be the original length of the spring. Then
`4=k(alpha-l),5=k(beta-l),9=k(gamma-l)`
`therefore (4)/(5)=(alpha-1)/(beta-1)or4beta-4l=5alpha-5lorl=5alpha-4beta" "...(i)`
Now `(9)/(4)=(gamma-1)/(alpha-l)or9alpha-9l=4gamma-4l`
or `4gamma=9alpha-5l=9alpha-5(5alpha-4beta)` (Using (i))
or `gamma=5beta-4alpha`