$A$ curved surface is shown in the figure. The portion $BCD$ is free of friction. There are three spherical balls of identical radii and masses. Balls are released from rest one by one from $A$,which is at a slightly greater height than $C$.
With the surface $AB$,ball $1$ has large enough friction to cause rolling down without slipping; ball $2$ has a small friction and ball $3$ has a negligible friction.
$(a)$ For which balls is total mechanical energy conserved?
$(b)$ Which ball$(s)$ can reach $D$?
$(c)$ For balls which do not reach $D$,which of the balls can reach back $A$?

(A-D) For ball $1$,the rolling is without slipping. The static friction force does no work on the ball,so there is no dissipation of energy. Thus,total mechanical energy is conserved.
For ball $3$,friction is negligible,so there is no work done by friction. Thus,total mechanical energy is conserved.
For ball $2$,there is kinetic friction which dissipates energy as heat. Thus,mechanical energy is not conserved.
$(b)$ Ball $3$ has no energy loss,so it can reach $D$ because $A$ is at a higher level than $C$. Ball $1$ converts some potential energy into rotational kinetic energy,and ball $2$ loses energy due to friction. Neither ball $1$ nor ball $2$ has enough energy to reach the peak $C$ and cross over to $D$.
$(c)$ Since balls $1$ and $2$ lose energy (ball $1$ to rotation,ball $2$ to heat),they cannot reach the same height as $A$ after passing $B$. Therefore,they cannot reach back to $A$.