Q. Five identical springs are used in the following three configurations. The time periods of vertical oscillations in configurations (i), (ii) and (iii) are in the ratio
A) $1\ :\sqrt{2}\ :\frac{1}{\sqrt{2}}$
B) $2\ :\ \sqrt{2}\ :\frac{1}{\sqrt{2}}$
C) $\frac{1}{\sqrt{2}}\ :2\ :1$
D) $2\ :\frac{1}{\sqrt{2}}\ :1$
Explanation
(a) $T \propto \frac{1}{\sqrt{k}} \Rightarrow T_{1}:T_{2}:T_{3} = \frac{1}{\sqrt{k}}:\frac{1}{\sqrt{k/2}}:\frac{1}{\sqrt{2k}} = 1:\sqrt{2}:\frac{1}{\sqrt{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.