A sphere of mass `m` and radius `r` rolls without slipping on the horizontal surface with speed `v`. During its motion it encounters a fixed rectangular block of height `h=(r )/(4)` as shown. The collision is inelastic. Find the angular speed of sphere immediately after collision. The body rolls without slipping.

Explanation

During collision, large impulsive forces are generated at contact point `A`, neglecting weight of sphere.
By the conservation of angular momentum about `A`
`mv(r-h)+(2)/(5)mr^(2)((v)/(r))=mv'r+(2)/(5)mr^(2)((v')/(r))`
`(3)/(4)mvr+(2)/(5)mvr=(7)/(5)mv'r`
`(23)/(20)mvr=(7)/(5)mv'r`
`v'=(23)/(28)v`
`omega'=(v')/(r)=(23)/(28r)`