Answer to Question #275911 in Physics for Elah

Question

a Christmas ball in a shape of 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.

Answer 1

The moment of inertia:

$$I=\frac25 mR^2.$$

The period:

$$T=2\pi\sqrt{\frac{I}{mgL}}=2\pi R\sqrt{\frac{2}{5gL}}=0.98\text{ s}.$$