Question

A thin uniform rod of length $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of

• A. $\frac{1}{3} \frac{\ell^{2}\omega^{2}}{g}$
• B. $\frac{1}{6} \frac{\ell\omega}{g}$
• C. $\frac{1}{2} \frac{\ell^{2}\omega^{2}}{g}$
• D. $\frac{1}{6} \frac{\ell^{2}\omega^{2}}{g}$

Answer 1

Answer: (D)

$\frac{1}{6} \frac{\ell^{2}\omega^{2}}{g}$

Answer 2

$T.E_{i}=T.E_{f}$ $\frac{1}{2}I\omega^{2}=mgh$ $\frac{1}{2}\times\frac{1}{3}m\ell^{2}\omega^{2}=mgh \Rightarrow h=\frac{1}{6} \frac{\ell^{2}\omega^{2}}{g}$