Force due to gravity along the plane downward =mgsinx where x the angle of inclination.
Due to friction, force upward will umgcosx where u is coefficient of friction.
Therefore, net force downward = mgsinx – umgcosx. ….i
Torque due to friction T = Rumgcosx where R is radius of the ring.
Also T=Ia/R where I is moment of inertia and for ring I = mR2. a is linear acceleration due to torque.
Now, Ia/R = Rumgcosx.
a = ugcosx. …..ii
From i and ii,
anet = (mgsinx – umgcosx)/m + a
= gsinx-ugcosx+ugcosx.
Therefore, anet = gsinx.
Given x = 30o. sinx = ½
Thus, anet = g/2.
