A thin uniform rod of mass `m` and length `l` is free to rotate about its upper end. When it is at rest, it receives an impulse `J` as its lowest point, normal to its length immediately after impact.

Options

A. The angular momentum of the rod is iL
B. The angular velocity of the rod is `3I//ml`
C. The kinetic energy of the rod is `3I^(2)//2m`
D. The linear velocity of the midpoint of the rod is `3//2`m

Answer

A, B, C, D

Explanation

About A, Angular impulse `=DeltaL rArr` If `(Ml^(2))/3 omega , omega = (3I)/(Ml)` and `L_(A) =Il`
`K=1/2(Ml^(2))/3 omega^(2) =1/2 (Ml^(2))/3 (9I^(2))/(M^(2)l^(2)) = (3I^(2))/(2M)`, `V_(CM) = l/2 omega = (3I)/(2M)`