1. the com purely translates

 

2. if pure rolling cond is considered when acc of com = 0

 

  = 0 as for pure rolling a = R

 

as  = 0,  = 0 (as  = I)

 

if not pure rolling then com's acc = 0 implies that there is no translatory motion,ie the body is in tranlational equillibrium but the body need not be in rotational equillibrium.

 

3. if the rod rotates with , then radial force is M(L/2)^2, so the clamp will be subjected to this force. the radius is taken as L/2 as the com of the rod is at a distance of L/2 from the clamp, M is the mass of the rod.