All Problems

Mechanical Oscillations

Problem 4.43

A pendulum is constructed as a light thin-walled sphere of radius \(R\) filled up with water and suspended at the point \(O\) from a light rigid rod (Fig. 4.11). The distance between the point \(O\) and the centre of the sphere is equal to \(l\). How many times will the small oscillations of such a pendulum change after the water freezes? The viscosity of water and the change of its volume on freezing are to be neglected.

Reveal Answer
 Will increase 1+2/5(R/l)2 times. It is taken into account here that the water (when in liquid phase) moves translationwise, and the system behaves as a mathematical pendulum\text { Will increase } \sqrt{1+2 /_{5}(R / l)^{2}} \text { times. It is taken into account here that the water (when in liquid phase) moves translationwise, and the system behaves as a mathematical pendulum}
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