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The time period of mass suspended from a spring is $T$. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be:
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Verified Answer
The correct answer is:
$\frac{T}{2}$
Let $K=$ force constant of spring and $K^{\prime}=$ force constant of each part then
$$
\begin{gathered}
\frac{1}{K}=\frac{4}{K^{\prime}} \\
\Rightarrow \quad K^{\prime}=4 K \\
\therefore \text { Time period }=2 \pi \sqrt{\frac{m}{4 K}} \\
=\frac{1}{2} \times 2 \pi \sqrt{\frac{m}{4 K}}=\frac{T}{2}
\end{gathered}
$$
$$
\begin{gathered}
\frac{1}{K}=\frac{4}{K^{\prime}} \\
\Rightarrow \quad K^{\prime}=4 K \\
\therefore \text { Time period }=2 \pi \sqrt{\frac{m}{4 K}} \\
=\frac{1}{2} \times 2 \pi \sqrt{\frac{m}{4 K}}=\frac{T}{2}
\end{gathered}
$$
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