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 ω. Its centre of mass rises to a maximum height of

Answer 1

(d) : The uniform rod of length l and mass m is swinging about an axis passing through the end. When the centre of mass is raised through h, the increase in potential energy is mgh. This is equal to the kinetic energy

= (1/2)Iω².

⇒ mgh = 1/2(m(l²/3)).ω²

Therefore, h = (l² . ω²)/6g.