Moment of inertia of uniform rod of mass M and length L about an axis through its centre and perpendicular to its length is given by 
. Now consider one such rod pivoted at its centre, free to rotate in a vertical plane. The rod is at rest in the vertical position. A bullet of mass 
moving horizontally at a speed v strikes and embedded in one end of the rod. The angular velocity of the rod just after the collision will be
Text Solution
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Initial angular momentum of the system = Angular momentum of bullet before collision 
.....(i)
let the rod rotates with angular velocity 
Final angular momentum of the system 
......(ii)
By equation (i) and (ii) 
or 
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