Question

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

• A. $\frac{k}{\sqrt{2}}$
• B. $\frac{k}{2}$
• C. k
• D. 2k

Answer 1

The correct option is D 2k

For a force F, the extension x in a spring of force constant k is given by
F = kx (i)
Now extension is propoptional to the length of the spring. When te 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
$F=k^{\prime }{x}^{\prime }=k^{\prime }\frac{x}{2}$ (ii)
Comparing (i) and (ii) we get k' = 2k.
Hence the correct choice is (d).