A solid sphere spinning about a horizontal axis with an angular velocity `omega` is placed on a horizontal surface. Subsequently it rolls without slipping with an angular velocity of :

Options

A. `(2omega)/(5)`
B. `(7 omega)/(5)`
C. `(2 omega)/(7)`
D. `omega`

Answer

C

Explanation

Initial sphere is slipping and finally it starts rolling during its motion `tau` about point of contact is zero. Angular momentum of sphere about point of contact remains conserved

`I omega= (I + MR^(2)) omega.`
`rArr (2)/(5) MR^(2) omega= ((2)/(5) MR^(2) + MR^(2)) omega rArr omega. = (2omega)/(7)`