A) \[2\pi \left( \frac{m}{K} \right)\]
B) \[2\pi {{\left\{ \frac{(YA+KL)m}{YAK} \right\}}^{1/2}}\]
C) \[2\pi \frac{mYA}{KL}\]
D) \[2\pi \frac{mL}{YA}\]
Correct Answer: B
Solution :
The wire may be treated as a string for which force constant \[{{k}_{1}}=\frac{Force}{Extension}=\frac{YA}{L}\ \ \ \left( \because Y=\frac{F}{A}\times \frac{L}{\Delta L} \right)\] Spring constant of the spring \[{{k}_{2}}=K\] Hence spring constant of the combination (series) \[{{k}_{eq}}=\frac{{{k}_{1}}{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}}=\frac{(YA/L)K}{(YA/L)+K}=\frac{YAK}{YA+KL}\] \[\because \]Time period \[T=2\pi \sqrt{\frac{m}{k}}=2\pi {{\left[ \frac{(YA+KL)m}{YAK} \right]}^{1/2}}\]You need to login to perform this action.
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