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

Answer

B

Explanation

`T=2pisqrt((m)/(k)),"but k"=(F)/(x)`
`=2pisqrt((m)/((F)/(x)))=2pisqrt((mx)/(F))`
`y=(FL)/(Ax) therefore F=(yAx)/(L)`
`therefore T=2pisqrt((mx)/((yAx)/(L))) therefore 2pisqrt((mL)/(yA))`