A solid uniform sphere rotating about its axis (with rotational kinetic energy ${\mathrm{\omega }}_0$) is placed on a rough horizontal plane without any translational push. Friction coefficient p is not same everywhere on the plane and it may differ even at each point. After sometime the sphere begins pure rolling with total kinetic energy E. Then:

• A

  $\mathrm{\omega }=2{\mathrm{\omega }}_0/5$

• B

  $\mathrm{\omega }=2{\mathrm{\omega }}_0/7$

• C

  $\mathrm{\omega }=5{\mathrm{\omega }}_0/7$

• D

  $\mathrm{\omega }$ cannot be expressed in terms ${\mathrm{\omega }}_0$