Two similar springs P and Q have spring constant `k_(p) and k_(Q)` such that `k_(p) gt k_(Q)` . They are stretched , first by the same amount (case a,) then by the same force (case b ) . The work done by the springs `W_(P) and W_(Q)` are related as , in case (a) and case (b) , respectively :

Options

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

Answer

B

Explanation

For case (a) : `x_(1) =x_(2) = x ` suppose
`(W_(P))/(W_(Q))=(1/2k_(P)x^(2))/(1/2K_(Q)x^(2))=(K_(P))/(K_(Q))`
But `K_(P) gt K_(Q)` is given ,
` :. W_(P) gt W_(Q)`
For Case (b) : `F_(1) = F_(2) = F `
For constant force
`W = (F^(2))/(2K) :. W prop 1/K `
` :. (W_(P))/(W_(Q)) = (K_(Q))/(K_(P))`
but , `K_(P) gt K_(Q) rArr W_(P) lt W_(Q)`
` :. W_(Q) gt W_(P)` .