An object of mass \(m\) is suspended at the end of a massless wire of length \(L\) and area of cross\(-\)section, \(A\). Young modulus of the material of the wire is \(Y\). If the mass is pulled down slightly its frequency of oscillation along the vertical direction is

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(A) \(f =\frac{1}{2 \pi} \sqrt{\frac{ YA }{ mL }}\)

Detailed explanation

An elastic wire can be treated as a spring with

\(K =\frac{ Y A }{\ell}\)

\(T =2 \pi \sqrt{\frac{ m }{ k }}\)

\(f=\frac{1}{2 \pi} \sqrt{\frac{k}{m}}=\frac{1}{2 \pi} \sqrt{\frac{Y A}{m \ell}}\)

Same subject

From JEE Mains