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 ?

Explanation

True.
Work done in case - I
`W_(1)=(1)/(2)kx^(2)`
Work done in case - II
`W_(2)=P.E_("final")-P.E_("initial")`
`=(1)/(2)k(2x)^(2)-(1)/(2)kx^(2)`
`=(1)/(2)k(4x^(2)-x^(2))=3((1)/(2)kx^(2))`
`therefore W_(2)=3W_(1)`
`therefore W_(1)=(W_(2))/(3)`
Therefore true.