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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 
 


A
13l2ω2g
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B
16lωg
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C
12l2ω2g
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D
16l2ω2g
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Solution

The correct option is C 16l2ω2g
The uniform rod of length l and mass m can swing about an axis passing through the end. When it is given angular velocity ω it starts rotating in vertical plane. When the centre of mass rises through height h, the kinetic energy decreases. 
Using conservation of mechanical energy K+U=0
(012Iω2)+(mgh)=0

   mgh=12(ml23).ω2
  h=l2.ω26g

Physics

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