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 w. Its centre of mass rises to a maximum height of –

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

Answer 1

Answer: (D)

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

Answer 2

$\because$ mgh_CM

= $\frac{1}{2}$Iw²

\ mgh_CM = $\frac{1}{2}.\frac{m\mathcal{l}^{2}}{3}.\omega^{2}$

̃ h_CM = $\frac{w^{2}\mathcal{l}^{2}}{6g}$