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` at its lowest point, normal to its length immediately after impact,

Options

A. the angular momentum of the rod is `Jl`
B. the agular velocity of the rod is `3J//ml`
C. the kinetic energy of the rod is `3J^(2)//2m`
D. the linear velociyt of the midpoint of the rod is `3J//2m`

Answer

A, B, C, D

Explanation

Angular momentum `=` linear momentum `xx` perpendiclar distance from te point of rotation
or `L=JI`
Also, `I=(ml^(2))/3`
`omega=L/I=(JI)/(ml^(2)//3)=(3J)/(ml)`
kinetic energy `=(L^(2))/(2l)`
`=(J^(2)l^(2))/(2(ml^(2))/3)=(3J^(2))/(2m)`
`v_(c)=omega1/2=(3J)/(2m)`