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Two springs have force constants k(1) " ...

Two springs have force constants `k_(1) " and " k_(2) (k_(1) gt k_(2))`. On which spring is more work done, if (i) they are stretched by the same force and (ii) they are stretched by the same amount ?

Text Solution

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(a) `W_(A)=1/2 k_(A)x^(2) " " :.k_(A) gt k_(B)`
`W_(B)=1/2 k_(B)x^(2) " " :.W_(A) gt W_(B)`
(b) `F=k_(A)x_(A)=k_(B)x_(B),W_(A)=1/2k_(A)((F)/(k_(A)))^(2)=(F^(2))/(2k_(A))`
Similarly `W_(B)=(F^(2))/(2k_(B)):. W_(B) gtW_(A)`
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