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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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The amount of work done to stretching distance x
`W_(1)=1/2k^(2) therefore k=(2W_(1))/x^(2)`
Total work done in stretchig the spring through a distance `2x "is" W_(2)=1/2k(2x)^(2)`
`W_(2)1/2((2W_(1))/ x^(2))4x^(2)=4W_(1)`
Extra work required to stretch the additional x distance is
`W=W_(2)-W_(1)=4W_(1)-W_(1)=3W^(1)`
`therefore W_(1)=1/3W`
Hence it is true.
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