Q.

One end of a long metallic wire of length L is tied to the ceiling. The other end is tied to massless spring of spring constant K. A mass m hangs freely from the free end of the spring. The area of cross-section and Young's modulus of the wire are A and Y respectively. If the mass is slightly pulled down and released, it will oscillate with a time period T equal to

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a

2πmK

b

2π(YA+KL)mYAK1/2

c

2πmYAKL

d

2πmLYA

answer is B.

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Detailed Solution

The wire may be treated as a string for which force constant  k1=ForceExtension=YAL   ∵Y=FA×LΔLSpring constant of the spring  k2=KHence spring constant of the combination (series)keq=k1k2k1+k2=(YA/L)K(YA/L)+K=YAKYA+KL∵Time period  T=2πmk=2π(YA+KL)mYAK1/2
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One end of a long metallic wire of length L is tied to the ceiling. The other end is tied to massless spring of spring constant K. A mass m hangs freely from the free end of the spring. The area of cross-section and Young's modulus of the wire are A and Y respectively. If the mass is slightly pulled down and released, it will oscillate with a time period T equal to