A spring has a certain mass suspended from it and its period for vertical oscillation is $T$. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillation is now
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(b) $T = 2\pi \sqrt {\frac{m}{k}} $.
Also spring constant $(k) \propto \frac{1}{{{\rm{Length (}}L)}}$, when the spring is half in length, then $k$ becomes twice.
$\therefore T' = 2\pi \sqrt {\frac{m}{{2k}}} $
$\Rightarrow \frac{{T'}}{T} = \frac{1}{{\sqrt 2 }} $
$\Rightarrow T' = \frac{T}{{\sqrt 2 }}$
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