A point mass m is suspended at the end of a massless wire of length l and cross section. If Y is the Young's modulus for the wire, obtain the frequency of oscillation for the simple harmonic motion along the vertical line.

Options

A. `(1)/(2pi)sqrt((LA m)/(Y))`
B. `(1)/(2pi)sqrt((YA)/(mL))`
C. `(1)/(2pi)sqrt((mY)/(AL))`
D. `(1)/(2pi)sqrt((AL)/(mY))`

Answer

B

Explanation

`Y=(mgL)/(A(Delta l)) therefore Delta l =(mgL)/(YA)`=extension
`therefore` Force constant `K=(mg)/(Delta l)=(mg xx YA)/(mgL)=(A Y)/(L)`
`therefore` The frequency of vertical oscillation (n) `=(1)/(2pi)sqrt((K)/(m))`
`therefore n=(1)/(2pi)sqrt((AY)/(Lm))`