Two similar springs `P` and `Q` have spring constants `K_(P)` and `K_(Q)`. They are stretched first by the same amount `(` case `a)`,then by the same force `(` case `b)`. The work done by the spring `W_(P)` and `W_(Q)` are relased as, in case `(a)` and case `(b)`, respectively.

Options

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

Answer

C

Explanation

Here, `K_(P)=K_(Q)`
In case `(a) : x_(1)=x_(2)=x.`
`:. (W_(P))/(W_(Q))=((1)/(2)K_(P)x^(2))/((1)/(2)K_(Q)x^(2))=(K_(P))/(K_(Q)) :. W_(P)gtW_(Q)`
In case`(b): F_91)=F_(2)=F,`
for constant force, `W=(F^(2))/(2K)`
`:.(W_(P))/(W_(Q))=((F^(2))/(2K_(P)))/((F^(2))/(2K_(Q)))=(K_(Q))/(K_(P)), :. W_(Q)gtW_(P)`