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A curved surface is shown in 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 ball which do not reach $D$, which of the balls can reach back $A$ ?
Solution
$(a)$ As ball $1$ is rolling down without slipping, no dissipation of energy is there, total mechanical energy remains unchanged. Hence, it is conserved.
Ball $3$ is having negligible friction hence, there is no loss of energy. For it also the total mechanical energy is conserved.
$(b)$ Ball $1$ gains rotational energy, ball $2$ loses energy due to friction. They cannot cross at $C$. Ball $3$ can cross over.
$(c)$ Ball $1$$2$ turn back before reaching$ C$. Because of loss of energy, ball $1$ and $2$ both cannot roll back to $A$.
