The copper piece shown on the right consists of two parts. The lower part is a solid hemisphere (radius ?) and the part one is a solid cylinder (same radius ? in the base and height of ?). The mass of the lower part is ?.

1.If ? = ?, find the location of CM (center of mass) of this object.

2.Suppose we now tilt the vertical axis of the object slightly away from the ?-axis by an angle ?. Write down the potential energy of the object when ? is very small. You may use the ?? -plane as the reference for potential energy. Is the equilibrium at ? = 0 stable?

3.If ? is fixed and ? can be varied, find the ratio of ? = ?/? when the equilibrium at ? = 0 is neutral.