A sphere of mass `M` and radius r shown in the figure on a rough horizontal plane. At some instant it has translational velocity `v_(0)`, and rotational velocity about centre `v_(0)//2r`. The percentage change of translational velocity after the sphere start pure rolling:

Options

A. `14.28%`
B. `7.14%`
C. `21.42%`
D. none

Answer

A

Explanation

Initial angular momentum
`L=2/5Mr^(2)((v_(0))/(2r))+Mrv_(0)=6/5Mrv_(0)` …………i
The angular mometum about `A` is
`=2/5Mr^(v/r)+Mrv=2/5Mr^(2)(v/r)+Mrv`……ii
`v=6/7v_(0)`.
`:. %` change of translation velocity
`=[(v_(0)-6/7v_(0))/(v_(0))]xx100=1/7xx100=1.428%`