Question

a 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 zero point 105 kg and 0.12 m respectively what will be its period of oscillation when slightly displaced from its equilibrium position?

Answer 1

The period of small oscillations of an object with mass and volume that cannot be ignored depends on the moment of inertia:

$$T=2\pi\sqrt{\frac{I}{mgh}}$$

The moment of inertia of such a system is 

$$I=mr^2+\frac{2}{3}mr^2=\frac{5}{3}mr^2$$

Assuming the hinge of the ball is at its surface, i.e., h = r, we have

$$T=2\pi\sqrt{\frac{5r}{3g}}=2\pi\sqrt{\frac{5\cdot0.12}{3\cdot9.8}}=0.90\ s$$