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Q.

One end of a long metallic wire of length L is tied to the ceiling. The other end is tied to a massless spring of spring constant k. A mass m hangs freely from the free end of the spring. The area of cross-section and the Young's modulus of the wire are A and Y respectively. If the mass is slightly pulled down and released, it will oscillate. Find the time period of oscillation.

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a

2πm(YA+kL)YAk

b

12πmYA+kLYAk

c

2πYAkmYA+kL

d

2πkLYAk+mYA

answer is A.

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Detailed Solution

Here, the wire can be considered as a spring of spring constant YAL.1keq=1k1+1k2⇒ keq=k1k2k1+k2=kYALk+YAL=YAkkL+YA⇒ T=2πmkeq=2πm(YA+kL)YAk
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