A point of mass m is suspended at the end of a massless wire of length l and cross-section A. If Y is the Young's modulus for the wire, obtain the frequency of oscillation for the simple harmonic motion along the vertical line.
[Hint: If x is the displacement of mass m from the equilibrium position then `Y = (stress)/(strain)= (F/A)/(x/l)` or `F = (YAx)/(l) and this force acts opposite to x. Now proceed as in example 3.

Options

A. `(1)/(2pi)sqrt((A)/(mLY))`
B. `(1)/(2pi)sqrt((YA^(2))/(mL^(3)))`
C. `(1)/(2pi)sqrt((YA)/(mL))`
D. `(1)/(2pi)sqrt((YL)/(m))`

Answer

C

Explanation

`K=(YA)/(L) Rightarrow T+2pisqrt((m)/(K)) Rightarrow 2pisqrt((ml)/(YA))`