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: (C)

$T =2 \pi \sqrt{\frac{ m }{ k }}$
When spring is cut in the ratio $1: 3$, the force constant of the longer part is $\frac{4 k }{3}$.
$\therefore T ^{\prime}=2 \pi \sqrt{\frac{3 m }{4 k }}=\frac{\sqrt{3}}{2} T$