A) \[\frac{1}{8\pi }\sqrt{{{k}_{1}}+{{k}_{2}}}\]
B) \[8\pi \sqrt{\frac{{{k}_{1}}+{{k}_{2}}}{{{k}_{1}}{{k}_{2}}}}\]
C) \[\frac{\pi }{2}\sqrt{{{k}_{1}}-{{k}_{2}}}\]
D) \[\frac{\pi }{2}\sqrt{\frac{{{k}_{1}}}{{{k}_{2}}}}\]
Correct Answer: B
Solution :
The two springs are in series. Therefore, the time period is \[T=2\pi \sqrt{\frac{m}{k}}=2\pi \sqrt{m\left( \frac{{{k}_{1}}+{{k}_{2}}}{{{k}_{1}}{{k}_{2}}} \right)}\] As \[m=16\,kg;\] \[T=8\pi \sqrt{\frac{{{k}_{1}}+{{k}_{2}}}{{{k}_{1}}{{k}_{2}}}}\]
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