A) \[\frac{T}{2}\]
B) \[(3/2)k\]
C) \[6k\]
D) \[\sqrt{{{K}_{1}}}:\sqrt{{{K}_{2}}}\]
Correct Answer: B
Solution :
\[T=2\pi \sqrt{\frac{m}{k}}\]. Also spring constant (k) µ\[\frac{1}{\text{Length (}L)}\], 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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