Question

A wire of negligible mass having uniform area of cross section \( A \) and Young modulus \( Y \) is used to suspend a point mass \( m \). The point mass executes simple harmonic motion in a vertical plane with a period \( T \), then the length of the wire is:

• A. \( L=\frac{TY^2A}{4\pi^2m} \)
• B. \( L=\frac{T^2YA}{4\pi m^2} \)
• C. \( L=\frac{TY^2A}{4\pi m^2} \)
• D. \( L=\frac{T^2YA}{4\pi^2m} \)

Hint:

For oscillations of a mass suspended from an elastic wire, the effective spring constant is \( k=\frac{YA}{L} \).

Answer 1

The Correct Option is D