A thin uniform bar lies on a frictionless horizontal surface and is free to move in any way on the surface. Its mass is $$0.16kg$$ and length is $$1.7m$$. Two particles of each of mass $$0.08$$ kg are moving on the same surface and towards the bar in the direction perpendicular to the bar, one with a velocity of $$10$$ $$m/s$$ and the other with velocity $$6$$ $$m/s$$. If collision between particles and bar is completely inelastic, both particles strike with bar simultaneously. The velocity of center of mass after collision is

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Infinity Learn · Accepted Answer

see fig  Applying the law of conservation of momentum, we $$getmv1+mv2=2m+m0vCM$$ ∴ $$vCM=mv1+mv22m+m0$$ or  $$vCM=0$$⋅$$08$$×$$10+0$$⋅$$08$$×$$6(0$$⋅$$16+0$$⋅$$16)$$ $$=1$$⋅$$280$$⋅$$32=4m/s$$

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