Question

A metre stick swinging in vertical plane about a fixed horizontal axis passing through its one end undergoes small oscillation of frequency $f_{0}$. If the bottom half of the stick were cut off, then its new frequency of small oscillation would become

• A. $f_{0}$
• B. $\sqrt{2} f_{0}$
• C. $2 f_{0}$
• D. $2 \sqrt{2} f_{0}$

Answer 1

Answer: (B)

$f_{0}=\frac{1}{2 \pi} \sqrt{\frac{m g l}{I}}$
where $l$ is the distance between point of suspension and centre of mass of the body.
Thus, for the stick of length $L$ and mass $m$,
$f_{0}^{\prime}=\frac{1}{2 \pi} \sqrt{\frac{m g \frac{L}{4}}{\frac{m}{2} \frac{(L / 2)^{2}}{12}}}$
$=\frac{1}{2 \pi} \sqrt{\frac{12 g}{L}}=\sqrt{2} f_{0}$