Two identical springs are connected to mass \(\mathrm{m}\) as shown \((\mathrm{k}=\) spring constant). If the period of the configuration in (a) is \(2 \mathrm{~S}\), the period of the configuration (b) is

• A

  \(\sqrt{2} \mathrm{~S}\)
• Correct answer
  B

  \(1 \mathrm{~S}\)
• C

  \(\frac{1}{\sqrt{2}} \mathrm{~S}\)
• D

  \(2 \sqrt{2} \mathrm{~s}\)

Solution

\(\begin{aligned} & \text {Hints: } \frac{\mathrm{T}_1}{\mathrm{~T}_2}=\sqrt{\frac{\mathrm{k}_2}{\mathrm{k}_1}} \Rightarrow \frac{2}{\mathrm{~T}}=\sqrt{\frac{2 \mathrm{k}}{\frac{\mathrm{k}}{2}}}=2 \\ & \therefore \mathrm{T}=1 \mathrm{~S}\end{aligned}\)

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