Please give the correct options with proper explanation for each correct options?

1 Answer
Nov 4, 2017

(A) and (B)

Explanation:

As the outer ring rolls without slipping therefore any point on the ring has linear velocity given by the equation for circular motion

#v=romega#

Point #O# is also the centre of mass of the ring

#:.|vecV_(cm)|=|vecV_O|=(3R)ω#

Because the ring rolls clockwise, from the figure velocity vector has the direction of #hati#
#:.vecV_(cm)=vecV_O=3Rωhat i#

Linear velocity of point #P# has two components.
1. #vecV_(cm)#
2. #vecV_(P_"disk cm")#

Point #P# as a part of Disk has magnitude of linear velocity #=Romega/2#
To ascertain direction of this component see figure below. We need to state unit vector in the direction of tangent at #P# and its #xand z# components as shown.
studyboard, edited

Total linear velocity of point #P#
#vec V_P=\vec V_(cm)+\vec V_(P_("disk cm"))=3R\omega\hat i+{\omega R}/{2}(cos30\hat k-sin30\hat i)#
#=>vec V_P=3R\omega\hat i+{omega R}/{2}(sqrt3/2hat k-1/2hat i)#
#=>vec V_P={11}/{4}Romegahat i+{sqrt3}/{4}Romega hat k#