# A frozen pendulum

**Classical Mechanics**Level 4

A pendulum is constructed as a light thin-walled sphere filled up with water and suspended from the ceiling by a rigid rod of negligible mass. The radius of the spherical container is R and the distance between the pivot point and the center of mass of the system is L. The period of small oscillations is \(T_{0}\). Due to a temperature drop in the room the water froze and the pendulum began to oscillate with a different frequency, corresponding to the period \(T_{1}\). Determine \(\frac{T_{1}}{T_{0}}\) if \(\frac{L}{R}=2 \). Neglect the viscosity (friction) of the water and the change of its volume after freezing.