Question

A sphere of mass `M` and radius `r` shown in figure slips on a rough horizontal plane. At some instant it has translational velocity `V_(0)` and rotational velocity about the centre `(v_(0))/(2r)`. Find the translational velocity after the sphere starts pure rolling.
.
A. `(5v_(0))/(7)`
B. `(6v_(0))/(7)`
C. `(3v_(0))/(4)`
D. `(3v_(0))/(5)`

Answer 1

By the conservation of angular momentum about `A`
`mv_(0)R+(2)/(5)mR^(2)(v_(0))/(2R)=mv_(c.m.)R+(2)/(5)mR^(2)((v_(c.m.))/(R ))`
`v_(c.m.)=(6v_(0))/(7)`