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. $\frac{l^2{\omega }^2}{3g}$
• B. $\frac{l^2{\omega }^2}{8g}$
• C. $\frac{l^2{\omega }^2}{2g}$
• D. $\frac{l^2{\omega }^2}{6g}$

Answer 1

The correct option is D $\frac{l^2{\omega }^2}{6g}$

By conservation of energy,
$\frac{1}{2}\left(\frac{m{\ell }^2}{3}\right){\omega }^2=$ $mgh$
$h=\frac{{\omega }^2{\ell }^2}{6g}$