A uniform stick of mass m and length l with `I=1/12 ml^(2)` spins around on a frictionless horizontal plane, with its CM stationary A mass M is placed on the plane, and the stick collides elastically with it, as shown (with the contact point being the end of the stick) What should be the ratio of m//M be so that after the collision the stick has translational motion but no rotational motion?

Answer

`0002`

Explanation

Conservation of Angular momentum about 'P'
`(ml)/12 omega =Mv_(2)l/2` …..(1)
conservation of linear Momentum
`0=mv_(1)+Mv_(2)` …..(2)
`e=(v_(2)-v_(1))/(l/2) omega` …….(3)
by using above equation
`M=m/2`