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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 :

l2 ω2/2g

l2 ω2/6g

l2 ω2/3g

l2 ω2/8g

Solution:

By conservation of energy,
1/2(ml2/3)ω2 = mgh
h = ω2 l2/6g