  We studied the dynamics of an object sliding down on a semi-sphere with
radius $R$. We consider the physical situation where the semi-sphere is free to
move over a horizontal surface. Also, we consider that all surfaces in contact
are friction-less. We analyze the values for the last contact angle
$\theta^\star$, corresponding to the angle when the object and the semi-sphere
detach one of each other, considering all possible scenarios with different
values of $m_A$ and $m_B$. We found that the last contact angle only depends on
the ratio between the masses, and it is independent of the acceleration of
gravity and semi-sphere radius. In addition, we found that the largest possible
value of $\theta^\star$ occurs for the case when the semi-sphere does not move.
On the opposite case, the minimum value of the angle occurs for $m_A \gg m_B$
occurring at the top of the semi-sphere.
