## Question

A spring of force constant *k* is cut into two equal halves. The force constant of each half is

### Solution

2*k*

For a force *F*, the extension *x* in a spring of force constant *k* is given by

*F* = *kx*

Now extension is proportional to the length of the spring. When the spring is cut into two equal halves, the extension *x**’* of each half, for a force *F* will be *x**’* = *x*/2. If *k**’* is the force constant of each half, we have

Comparing (i) and (ii) we get

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