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A spring which is initially in un-streat...

A spring which is initially in un-streatched condition, is first stretched by a length x and again by a further length x. The work done in the first case `W_(1)` is one third of the work done in second case `W_(2)`. True of false ?

Text Solution

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Work done in the first case `W_(1)=(1)/(2)kx^(2)`. (i.e. P.E. stored)
In second case, work done `W_(2)` = Change in P.E.
`= P.E_(("final"))-PE_("initial")`
`=(1)/(2)k (2x)^(2)-(1)/(2)kx^(2)=(1)/(2)k(4x^(2)-x^(2))`
`W_(2)=(1)/(2)k 3x^(2)`
`W_(2)=3. W_(1)`
`therefore W_(1)=(1)/(3)W_(2)`
= True.
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