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. (a)`5beta-4alpha`
B. (b)`beta-alpha`
C. (c)`5alpha-4beta`
D. (d)`9(beta-alpha)`

Answer

A

Explanation

Let the natural length of the spring `= l_(0)`
From figure

`4 = k (alpha - l_(0))`…..(i)
`5 = k(beta - l_(0))`….(ii)
`9 = k(gamma - l_(0))`…..(iii)
eq. `((iii) - (i))/((iii) - (ii)) rArr (5)/(4) = (k(gamma - alpha))/(k(gamma - beta))`
`gamma = 5beta - 4 alpha`