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Let the two springs A and B be such that...

Let the two springs A and B be such that`K_(A)gtK_(B)` , On which spring will more work has to be done if they are stretched by the same force ?

Text Solution

Verified by Experts

`F=k_(A)x_(A)=K_(B)x_(B)`
`x_(A)=F/K_(A), X_(B)=F/K_(B)`
The work done on the spring are stored as potentail enery in the springs.
`U_(A)/U_(B)=(K_(A)x_(A)^(2))/(K_(B)x_(B)^(2))=(K_(A)(F/K_(A)^(2)))/(K_(B)(F/K_(B)^(2)))=(1/K_(A))/(1/K_(B)`
`U_(A)/U_(B)=K_(B)/K_(A)`
`K_(A)gtK_(B)` implies that `U_(B)gtU_(A)`. Thus , more work is done on B than A.
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