Q. 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
A) $\frac{T}{2}$
B) $\frac{T}{\sqrt{2}}$
C) $\sqrt{2}T$
D) $2T$
Explanation
(b) $T = 2\pi\sqrt{\frac{m}{K}}.$ Also spring constant $(K) \propto \frac{1}{Length\ (l)},$
when the spring is half in length, then $K$ becomes twice
$\therefore T^{'} = 2\pi\sqrt{\frac{m}{2K}} \Rightarrow \frac{T^{'}}{T} = \frac{1}{\sqrt{2}} \Rightarrow T^{'} = \frac{T}{\sqrt{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.