A) \[T={{T}_{1}}+{{T}_{2}}\]
B) \[T=\frac{{{T}_{1}}{{T}_{2}}}{{{T}_{1}}+{{T}_{2}}}\]
C) \[{{T}^{2}}={{T}_{1}}^{2}+{{T}_{2}}^{2}\]
D) \[\frac{1}{{{T}^{2}}}=\frac{1}{{{T}_{1}}^{2}}+\frac{1}{{{T}_{2}}^{2}}\]
Correct Answer: D
Solution :
[d] \[{{T}_{1}}=2\pi \sqrt{\frac{m}{{{k}_{1}}}}\Rightarrow {{k}_{1}}=\frac{4{{\pi }^{2}}m}{T_{2}^{2}}\] \[{{T}_{2}}=2\pi \sqrt{\frac{m}{{{k}_{2}}}}\Rightarrow {{k}_{2}}=\frac{4{{\pi }^{2}}m}{T_{2}^{2}}\] Now \[T=2\pi \sqrt{\frac{m}{k}}\] \[k=\frac{4{{\pi }^{2}}m}{{{T}^{2}}}\] in parallel \[k={{k}_{1}}+{{k}_{2}}.\]
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