A) \[{{T}^{2}}=T_{1}^{2}+T_{2}^{2}\]
B) \[{{T}^{-2}}=T_{1}^{-2}+T_{2}^{-2}\]
C) \[{{T}^{-1}}={{T}_{1}}^{-1}+{{T}_{2}}^{-1}\]
D) \[T={{T}_{1}}+{{T}_{2}}\]
Correct Answer: B
Solution :
\[{{T}_{1}}=2\pi \sqrt{\frac{m}{{{k}_{1}}}},{{T}_{2}}=2\pi \sqrt{\frac{m}{{{k}_{2}}}}\] \[T=2\pi \sqrt{\frac{m}{({{k}_{1}}+{{k}_{2}})}}\] \[{{T}_{1}}^{-2}+{{T}_{2}}^{-2}=\frac{{{k}_{1}}}{4{{\pi }^{2}}m}+\frac{{{k}_{2}}}{4{{\pi }^{2}}m}\] \[=\frac{{{k}_{1}}+{{k}_{2}}}{4{{\pi }^{2}}m}\] \[={{T}^{-2}}\] Hence, the correction option is [b].You need to login to perform this action.
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