Question

A christmas ball in a shape of a hollow sphere is hung from the tree by a piece of trade attached to the surface of the ball the mass and radius of the tall are 0.105 kg and 0.12 m respectively what will be its period of rotation when slightly displaced from its equilibrium position

Answer 1

The period of oscillation is

$$T=2\pi\sqrt{\frac{I}{mgL}},\\\space\\ T=2\pi \sqrt{\frac{\frac25mR^2}{gL}},\\\space\\ T=2\pi R\sqrt{\frac{2}{5gL}}=2\pi ·0.12\sqrt{\frac{2}{5·9.8·0.12}}=0.44\text{ s}.$$