Question

Two springs have force constants `K_(1)` and `K_(2)` , where `K_(1)gtK_(2)`. On which spring, more work is downe if
(i) they are stretched by the same force?
(ii) they are stretched by the same amount?

Answer 1

(a) As `W=(1)/(2)Kx^(2)` and `K_(A) gt K_(B)`
`:.` work done on spring A will be more than work done on spring B (for same x)
(b) As `F=Kx`, therefore, `x=F//K`
As `K_(A) gt K_(B) :. x_(A) lt x_(B)`
As `W=(1)/(2)Kx^^(2)=(1)/(2)((F)/(x))x^(2)=(1)/(2)Fx`
i.e., more work is required in case of spring B than in the case of spring A.