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A bullet of mass m moving with a velocit...

A bullet of mass `m` moving with a velocity of `u` just grazes the top of a solid cylinder of mass `M` and radius `R` resting on a rough horizontal surface as shown and is embedded in the cylinder after impact. Assuming that the cylinder rolls without slipping, find the angular velocity of the cylinder and the final velocity of the bullet.

Text Solution

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Let v and be the velocity of bullet and angular velocity of cylinder respectively. Applying conservation of angular moment about the point of contact of cylinder with floor,`m u.2R=m u.2R+(I_(CM)+MR^2)omega` Here, `v=2RomegaandI_(CM)=1/2MR_2`Substituting and solving, we get `v=(8m u)/(8m+3M) and omega =(4m u)/((83+3M)R^dot`.
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