One end of a long metallic wire of length L i | vedclass

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(B) The wire acts as a spring with a force constant $k_1$. From the definition of Young's modulus $Y = \frac{F/A}{\Delta L/L}$,we get $k_1 = \frac{F}{

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$2\pi \sqrt{\frac{(YA + KL)m}{YAK}}$

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(B) The wire acts as a spring with a force constant $k_1$. From the definition of Young's modulus $Y = \frac{F/A}{\Delta L/L}$,we get $k_1 = \frac{F}{\Delta L} = \frac{YA}{L}$.The spring constant of the given spring is $k_2 = K$.Since the wire and the spring are in series,the equivalent spring constant $k_{eq}$ is given by $\frac{1}{k_{eq}} = \frac{1}{k_1} + \frac{1}{k_2}$.$\frac{1}{k_{eq}} = \frac{L}{YA} + \frac{1}{K} = \frac{KL + YA}{YAK}$.Therefore,$k_{eq} = \frac{YAK}{YA + KL}$.The time period of oscillation is $T = 2\pi \sqrt{\frac{m}{k_{eq}}} = 2\pi \sqrt{\frac{m(YA + KL)}{YAK}}$.

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