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Physics

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    $\begingroup$ You went wrong by assuming that the work done on both of them is the same. You need to prove this assumption. $\endgroup$ Commented Sep 7, 2017 at 2:27
  • $\begingroup$ I din't want to use mathematics in my answer or a formal justification, but I believe it can be easily proved by considering that each spring is acted upon by a spring force due to another spring and force applied by us. Also the displacement is exactly same, which implies that work done on both the springs is equal. $\endgroup$ Commented Sep 7, 2017 at 12:30
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    $\begingroup$ Imagine one is a much stiffer spring, now the displacement is the same but the work is not equal. How do you know that is not also true of identical springs? Probably because you were thinking about Hooke's law, but you can't assume Hooke's law in order to justify Hooke's law. $\endgroup$ Commented Sep 7, 2017 at 20:03