Question

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. $\sqrt{3}T$

Answer 1

Answer: (B)

$\frac{T}{\sqrt{3}}$

Answer 2

The spring mass system oscillate in $SHM$, its time period is given by $T=2 \pi \sqrt{\frac{m}{k}}$ When spring is cut into ratio $1: 3$, the new time constant is $k^{\prime}=3 k$ $\therefore \frac{T}{T^{\prime}}=\sqrt{\frac{3 k}{k}} \Rightarrow T^{\prime}=\frac{T}{\sqrt{3}}$