Question

A spring block system in horizontal oscillation has a time-period $T$. Now the spring is cut into four equal parts and the block is re-connected with one of the parts. The new time period of vertical oscillation will be

• A. $\frac{T}{\sqrt{2}}$
• B. $2 T$
• C. $\frac{T}{2}$
• D. $\frac{T}{2 \sqrt{2}}$

Answer 1

Answer: (C)

When spring is cut into $4$ parts.
The spring constant of each part will become $4 \,k$.
$T_{2}=2 \pi \sqrt{\frac{m}{4 k}}$
$T_{2}=\frac{T}{2}$