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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 mass less 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. Find the time period with which mass m will oscillate if it is slightly pulled down and released

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a

2πAYKmAY +KL

b

2πmAY +KLAYK

c

2πmYKAY +KL

d

2πmAYLAY +KL

answer is B.

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Detailed Solution

elongation in the wire e=FLAY          F=AYLe equivalent sprng constant  k1= AYL along with this a spring of force constant K is connected in series then 1Ke= 1k1+1K= LAY+1K time period T=2π1Ke
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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 a mass less 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. Find the time period with which mass m will oscillate if it is slightly pulled down and released