21 22 A thin rod of mass m and length L lies on a frictionless...
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21 22 A thin rod of mass m and length L lies on a frictionless horizontal surface and is hinged at one of its ends such that it can rotate freely about a vertical axis passing through the hinge A particle of same mass m hits the rod at the extreme end as shown with velocity vo and does not stick with rod and come to rest immediately such that the rod rotates with a constant angular velocity w after the collision 1 Then angular velocity just after collision is equal to 3v0 L A 2v0 5L A B 2 Magnitude of hinge reaction just after the collision is 7mv 5mv 2L 2L B C C 5vo 7L 9mv 2L D D 5vo 9L 9mv 4L N s m
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To solve the problem we can break it down into two parts finding the angular velocity just after the collision and determining the magnitude of the hinge reaction 1 Angular Velocity Just After Collision Given Mass of the rod m Length of the rod L Mass of the particle m Initial velocity of the particle v0 Conservation of Angular Momentum Before the collision the angular momentum of the system about the hinge point is due to the particle only as the rod is
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