Q. Time period of a spring mass system is $T$. If this spring is cut into two parts whose lengths are in the ratio 1:3 and the same mass is attached to the longer part, the new time period will be
A) $\sqrt{\frac{3}{2}}\ T$
B) $\frac{T}{\sqrt{3}}$
C) $\frac{\sqrt{3}T}{2}$
D) $\sqrt{3}T$
Explanation
(b) The spring-mass system oscillates in SHM, its time period is given by
$T = 2\pi\sqrt{\frac{m}{k}}$
When spring is cut in ratio 1:3, the new time constant is $k^{'} = 3k$
$\therefore$ $\frac{T}{T'} = \sqrt{\frac{3k}{k}}$
$\Rightarrow$ $T^{'} = \frac{T}{\sqrt{3}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.