A cantilever beam of cross section A, moment of inertia I and length L is having natural frequency $$ω_1$$​. If the beam is accidentally broken into two halves, the natural frequency of the remaining cantilever beam ω2 will be such that it

Correct option is A

​$$\begin{aligned}&\text{The natural frequency of the remaining half-length cantilever beam } (\omega_2) \text{ will be \textbf{four times} the original frequency } (\omega_1): \\&\omega_2 = 4 \omega_1 \\[1em]&\textbf{Key Points:} \\[0.5em]&1.\ \textbf{Length Dependency:} \text{ The natural frequency scales as } \frac{1}{L^2}. \text{ Halving the length \textbf{quadruples} the frequency.} \\[0.5em]&2.\ \textbf{Assumptions:} \\&\quad \circ \text{ The beam is homogeneous and prismatic.} \\&\quad \circ \text{ No additional mass or damping is introduced after breaking.} \\[0.5em]&3.\ \textbf{Practical Implications:} \\&\quad \circ \text{ Shorter beams vibrate at higher frequencies, which is critical in structural design and failure analysis.}\end{aligned}$$​​