Question

A point mass $M$ is suspended at the end of a mass less wire of length $L$ and cross-section $A$. If $Y$ is the Young's Modulus for the wire, the time period oscillation for the S.H.M. along the vertical line is

• A. $T=\frac{1}{2\pi }\sqrt{\frac{ML}{YA}}$
• B. $T=2\pi \sqrt{\frac{YL}{MA}}$
• C. $T=\frac{1}{2\pi }\sqrt{\frac{MA}{YL}}$
• D. $T=2\pi \sqrt{\frac{ML}{YA}}$

Answer 1

The correct option is D $T=2\pi \sqrt{\frac{ML}{YA}}$

Equivalent stiffness of wire $K=\frac{YA}{L}$

$\therefore$ $T=2\pi \sqrt{\frac{M}{K}}$

$\Rightarrow T=2\pi \sqrt{\frac{ML}{YA}}$