Its JEE Advanced Exam- for entry into undergrad engineering.
and the molecule won't go upto the highest point as per KE because of viscosity isn't it? Viscosity'll retard it..
I just did
##T## = 2/5 M R^2 * α
which gives α =5μg/ 2R
hence
##w_0(f)## = ##w_0(i)## - α t
i.e 0= ##v_0##/2R - 5μg/ 2R *t
hence i got t=4##v_0##/5μg (time when rotation ceases)
I found out the time when rotation ceases to be 4 ##v_0## /5*mew*g, where mew=coefficent of friction of surface but I am unable to plot the graph post that time