A) k
B) \[\frac{k}{2}\]
C) 2 k
D) 4 k
Correct Answer: C
Solution :
From force law \[F=-kx\] ... (i) where k is force constant or spring constant of spring and x is the extension or compression in spring. \[\Rightarrow \] \[k=\frac{F}{x}\] or \[k\propto \frac{1}{x}\] or \[\frac{{{k}_{1}}}{{{k}_{2}}}=\frac{{{x}_{2}}}{{{x}_{1}}}\] ?. (ii) If spring is divided in two parts, then \[{{x}_{1}}=x,\,{{x}_{2}}=\frac{x}{2},\,{{k}_{1}}={{k}_{2}}\] \[\therefore \] \[\frac{k}{{{k}_{2}}}=\frac{x/2}{x}\] or \[{{k}_{2}}=2\,k\] Hence, spring constant will be doubled.
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