One end of a long metallic wire of length (L) is tied to the ceiling. The other end is tied to a massless 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. If the mass is slightly 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

C

Explanation

For two springs in series, the equivalent spring constant is `k_(eq)=(k_(1)k_(2))/(k_(1)+k_(2))`
Here, `k_(1)=kandk_(2)=(YA)/(L)`
`therefore k_(eq)=((kYA)/(L))/(k+(YA)/(L))=(kYA)/(kL+YA)therefore T=2pisqrt((m)/(k_(eq)))=2pisqrt((m(YA+kL))/(YAk))`