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)    $2\mathrm{\pi }\left(\frac{\mathrm{m}}{\mathrm{K}}\right)$                   (b)     $2\mathrm{\pi }{\left\{\frac{\left(\mathrm{YA}+\mathrm{KL}\right)\mathrm{m}}{\mathrm{YAK}}\right\}}^{1/2}$

(c)    $2\mathrm{\pi }\frac{\mathrm{mYA}}{\mathrm{KL}}$                (d)      $2\mathrm{\pi }\frac{\mathrm{mL}}{\mathrm{YA}}$

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

Spring constant of the spring ${k}_{2}=K$

Hence spring constant of the combination (series)

$⊝$Time period

Difficulty Level:

• 10%
• 68%
• 12%
• 12%