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?
A. `W_(P) = W_(Q) , W_(P) gt W_(Q)`
B. `W_(P) = W_(Q) , W_(P) = W_(Q)`
C. `W_(P) = W_(Q) , W_(Q) gt W_(P)`
D. `W_(P) lt W_(Q) , W_(Q) lt W_(P)`

Answer 1

Case (a), : Spring are streched by the same amount
The work done by the springs `W = (1)/(2) Kx^(2)`
Hence `W prop K`
As `K_(P) gt K_(Q)` it means `W_(P) gt W_(Q)`
Case (b) Spring are streched by the same force
`F = K_(P) X_(P) = K_(Q) X_(Q)`
The work done by the spring
`W = (1)/(2)Kx^(2) = (1)/(2) K ((F)/(K))^(2) = (1)/(2) (F^(2))/(K)`
Hence `W = (1)/(K)` it means `W_(Q) gt W_(P)`