A light, cubical container of volume a3 is initially filled with a liquid of mass density 6. The cube is initially supported by a light string to form a simple pendulum of length Li, measured from the center of mass of the filled container, where Li >> a. The liquid is allowed to flow from the bottom of the container at a constant rate (dM/dt). At any time t, the level of the fluid in the container is h and the length of the pendulum is L (measured relative to the instantaneous center of mass).
(a) Sketch the apparatus and label the dimensions a, h, Li, and L.
(b) Find the time rate of change of the period as a function of time t.
(c) Find the period as a function of time.