A mass (m) is suspended at the end of a weightless wire of length L, cross-sectional area A and Young's modulus Y. The period of oscillation for the S.H.M. along the vertical direction is

Options

A. `2pi sqrt((YA)/(mL))`
B. `2pisqrt((mL)/(YA))`
C. `2pi sqrt((mY)/(AL))`
D. `2pi sqrt((AL)/(mY))`

Answer

B

Explanation

`Y=(MgL)/(Ae) therefore e=(MgL)/(YA)`
Force constant, `K=(Mg)/(e )=(MgYA)/(MgL)=(YA)/(L)`
`therefore T=2pisqrt((m)/(K))=2pisqrt((mL)/(YA))`