Answer to Question #158204 in Physics for Mark

Question

Christmas ball in a shape of a hollow sphere is hung from the tree by a

piece of thread attached to the surface of the ball. The mass and radius of

the ball are 0.105kg and 0.12m, respectively. What will be its period of

oscillation when slightly displaced from its equilibrium position? (Hint: /5/3mr2

Answer 1

First, find the moment of inertia of the hollow ball:

$$I=\frac23 mr^2.$$

The period of oscillations of such a sphere slightly displaced from equilibrium position is

$$T=2\pi\sqrt{\frac{I}{mgh}}=2\pi\sqrt{\frac{I}{mgr}}=\\\space\\ =2\pi\sqrt{\frac{2r}{3g}}=0.57\text{ s}.$$