The correct option is C 32MR2ω
For pure rolling, v=Rω
where, v= linear velocity of COM of disc.
ω= angular velocity of disc.
⇒Angular momentum about origin will include the angular momentum due to translation as well as angular momentum due to rotational motion.
∴→L0=→LTrans+→LRot
Angular momentum about origin O is given by (L0)
⇒L0=MvCMR+ICMω
∵ICM=MR22 and vCM=Rω
So, L0=M(Rω)R+(MR22×ω)
+ve sign taken since both angular momentums have a clockwise sense about origin O.
∴L0=32MR2ω