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Question

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 modules of the wire A and Y, respectively. If the mass is slightly pulled down and released, it will oscillate with a time period T equal to :

A
2πmK
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B
2πm(YA+KL)YAK
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C
2πmYAKL
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D
2πmLYA
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Solution

The correct option is A 2πmK
Time period of oscillation will only depend upon, Tension in spring at attached point block . Metallic wire won't effect Time period of block
T=Kx

so Time period is of such system is given by

T=2πmk

where k=K in this case.

T=2πmK

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