How Does a Leaking Cubical Pendulum Affect Its Period?

[kashiark]

Homework Statement

There is a cubical pendulum with a side of 2a filled with water that is leaking at a constant rate. Determine the period of the pendulum in terms of variables.

Homework Equations

T = 2π√(l/g)
v = s³ for a cube
v = s²h for a rectangle

The Attempt at a Solution

v=s²h
v=4a²h
The length varies with the new center of mass which is h/2, so l = h/2.
v=8a²l
differentiate with respect to time and
dv/dt = 8a²dl/dt
dl/dt = 1/(8a²)dv/dt
to avoid the problem from looking too complicated, let's set dv/dt = r
l_i= initial length
T = 2π√((l_i-(rt/(8a²)))/g)

I multiplied by time so that we would be left with the change in length, and I subtracted it because dl/dt is negative, and the length should obviously be increasing. Is this right?

 

[rl.bhat]

It is correct.