Q117 / 200 · NEET 2003 · Physics

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:

  • A
    $\frac{T}{4}$
  • B
    $T$
  • Correct answer
    C
    $\frac{T}{2}$
  • D
    $2 T$

Solution

Let $K=$ force constant of spring and $K^{\prime}=$ force constant of each part then $$ \begin{gathered} \frac{1}{K}=\frac{4}{K^{\prime}} \\ \Rightarrow \quad K^{\prime}=4 K \\ \therefore \text { Time period }=2 \pi \sqrt{\frac{m}{4 K}} \\ =\frac{1}{2} \times 2 \pi \sqrt{\frac{m}{4 K}}=\frac{T}{2} \end{gathered} $$

Hence, the correct answer is option: 'C'.

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