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Two similar springs P and Q have spring ...

Two similar springs P and Q have spring constants `K_(P)andK_(Q)`, such that `K_(P)gtK_(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)andW_(Q)` are related as, in case (a) and case (b), respectively

A

`W_(P)=W_(Q),W_(P)gtW_(Q)`

B

`W_(P)=W_(Q),W_(P)=W_(Q)`

C

`W_(P)gtW_(Q),W_(Q)gtW_(P)`

D

`W_(P)ltW_(Q),W_(Q)ltW_(P)`

Text Solution

Verified by Experts

The correct Answer is:
C
Work done by the spring (W)
= change in potential energy
= `1/2Kx^(2)` [x = increase in length]
Case a : The increase in length is same for P and Q.
Then, `W_(P)=1/2K_(P)x^(2)andW_(Q)=1/2K_(Q)x^(2)`
`therefore" "W_(P)gtW_(Q)`
Again, if F is the applied force, then spring constant,
`K=F/xor,x=F/K`
`therefore" "W=1/2K(F/K)^(2)=1/2F^(2)/K`
Case b : `W_(P)=1/2F^(2)/K_(P)andW_(Q)=1/2F^(2)/K_(Q)`
`therefore" "W_(Q)gtW_(P)`
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