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 slighty pulled down and released , it will oscillate with a time period T equal to

Options

A. `2pisqrt((m)/(k))`
B. `2pisqrt((m(YA+kL))/(YAK))`
C. `2pisqrt((mYA)/(kL))`
D. `2pisqrt((mL)/(YA))`

Answer

B

Explanation

(b) Wire is equivalent to a spring of spring constant, `k'=(AY)/(L)`
k' and k are in series
`k_(eq)=(k'k)/(k'+k)=((AY//L)+k)/(((AY)/(L))+k)=(AYk)/(AY+kL)`
`T=2pisqrt((m)/(k_(eq)))=2pisqrt((m(AY+kL))/(AYk))`