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Q.

A thin rod of mass 0.9 kg and length 1 m is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of mass 0.1 kg moving in a straight line with velocity 80 m/s hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in rad/s) of the rod immediately after the collision will be____

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Detailed Solution

Applying conservation of angular momentum of particle + rod about the hingeLi=Lf​⇒muL +Irodwinitial=Iparticle+Irodωfinal​⇒m×u×L+0=mR2+MR23ω​⇒1×0.1×80+0=0.1×12+0.9×123ω​⇒8=0.4ω​⇒ω=20 rad/s
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