If a mass of liquid in gravity free space is in equilibrium, then it has the form of a sphere, stabilised by its own surface tension (see given Figure(left)).
Suppose that the mass now rotates like a rigid body with constant angular velocity. What will its equilibrium shape be now? Show that, as the angular speed increases, the mass becomes more oblate until its top and bottom surfaces become quite flat (Figure given(centre)).
Show further that, at higher angular speeds, the top and bottom surfaces approach each other until they meet (Figure given (right)) and the mass breaks up.
Find this critical angular speed for a sphere of mercury of radius 5 cm.
