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 is 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                   (b)     2πYA+KLmYAK1/2

(c)    2πmYAKL                (d)      2πmLYA

Concept Videos :-

#23-Torsional Pendulum
#24-Oscillations of Spring Block System
#25-Combination of Springs
#26-Combination of String Spring
#27-Inclined Spring
#28-Spring Pulley System
#29-Solved Examples 9
#30-Solved Examples 10
#31-Special Case of Spring Block System
#32-Spring with Mass Coupled Oscillator

Concept Questions :-

Combination of springs

b)  The wire may be treated as a string for which force constant                                                         k1=ForceExtencion =YALY=FA×LL

   Spring constant of the spring k2=K

Hence spring constant of the combination (series)

keq=k1k2k1-k2=(YA/L)KYA/L+K =YAKYA+KL

Time period T=2πmk=2πYA+ KLmYAK1/2

    

Difficulty Level:

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